Buff Toddy
The only you way Toddy is going to make a difference is by using your party's assets to strengthen him. Toddy will miss most attacks. Best way to make him actually hit is the Archery fighting style, but then he's only dealing 7-10 damage on average (depending on the archetype. This is still probably the best build, but isn't going to make Toddy particularly powerful). Try these out:
Magic Items
There are some magic items that will let Toddy punch above his weight class. If you have access to some simple items like the wand of magic missles (which you don't need to be a spellcaster to use), he will have some effectiveness even as a non-caster. But picking up Eldritch Knight and grabbing a wand of fireballs would be very effective (about 5 fireballs per day). You can avoid needing to pick up Eldritch Knight for spellcasting requirements by using the half-elf High or Drow variants.
Tentacle Rod. This rod with a shield would be very strong. It gives you 3 attacks with a +9 attack bonus. You do have to be closer to the front (15 feet range), so it is risky, but Toddy's damage output would be great compared to other builds.
Spells
Some spells allow other creatures to make attacks using the original caster's modifiers. These spells let Toddy basically attack as a Tier 3 character when cast by your party. Magic stone says:
If someone else attacks with the pebble, the attacker adds your spellcasting ability modifier, not the attacker's, to the attack roll. On hit, the target takes bludgeoning damage equal to 1d6 + your spellcasting ability modifier.
A Battle Master with a sling and these stones could make good use of the +5 spellcasting ability modifiers of your party and still use his maneuvers (such as Commander's Strike).
Another really strong spell for this purpose is dragon's breath:
Until the spell ends, the creature can use an action to exhale energy of the chosen type in a 15-foot cone. Each creature in that area must make a Dexterity saving throw, taking 3d6 damage of the chosen type on a failed save, or half as much damage on a successful one.
This spell turns Toddy into a breath weapon that packs a punch. If you plan on using this spell often though, you will want a durable Toddy (so focus on plate armor, a shield (preferably magic ones), and maybe grab Eldritch Knight for the clutch casts of the shield spell).
Help Toddy Live
This is going to be the hardest part, as some enemies will be able to kill Toddy outright from full health, and most enemies can kill him outright if he's damaged. There are a few ways to prevent him dying outright (so you can at least stabilize him if he falls).
The aid spell will increase his maximum HP (which proportionally is ridiculous if upcast while he's at this low level).
Choose up to three creatures within range. Each target’s hit point maximum and current hit points increase by 5 for the duration.
At Higher Levels: When you cast this spell using a spell slot of 3rd level or higher, a target’s hit points increase by an additional 5 for each slot level above 2nd.
With a 7th level spell slot (if one of your teammates can part with it), this doubles the HP of Toddy and provides a good buff to two other party members as well. Even a 3rd level spell slot, helps greatly to mitigate instant death. Your other option is death ward.
The first time the target would drop to 0 hit points as a result of taking damage, the target instead drops to 1 hit point, and the spell ends.
This is especially useful for Toddy because he will be dropping to 0 fast, so this will definitely proc (whereas it may never proc on one of your party members who have more HP and healing options).
If you are not using the dragon's breath method, then just keep Toddy in the back. He still will benefit from aid and death ward, but he will take much less assault and a Battlemaster with a bow is almost as good as one with a sword. Just have him pepper a couple arrows (preferably from a magic bow, so they aren't block by magic resistant creatures), and let him command you to sneak attack on his turn.\
Note: even with an archer build, you want to make sure he has enough strength for Plate armor
Also, if you have one, make sure he is in range of the paladin's auras so he is much more likely to succeed on saving throws.
Whenever you or a friendly creature within 10 feet of you must make a saving throw, the creature gains a bonus to the saving throw equal to your Charisma modifier (with a minimum bonus of +1). You must be conscious to grant this bonus.
It might even be worth it to have the paladin sit back more and used ranged attacks unless he needs the smites to help protect Toddy (unless Toddy will be safe enough only 15 feet from the enemies, such as in a narrow chamber).
If you will be in foliage or other natural obscurers often, grabbing the Variant Half-Wood Elf would be very strong for Mask of the Wild:
You can attempt to hide even when you are only lightly obscured by foliage, heavy rain, falling snow, mist, and other natural phenomena.
If using this build, it is better to drop your armor down to Breastplate and put Toddy's first level-ups in rogue for Cunning Action.
Toddy's levels
Toddy will reach the first few early levels very quickly, so while it is tempting to grab level 5 for the extra attack, this is not a good idea. You should expect Toddy to die, so I would immediately rush Barbarian to grab the Path of the Zealot at level 7. This will give you Warrior of the Gods which says:
If a spell, such as raise dead, has the sole effect of restoring you to life (but not undeath), the caster doesn’t need material components to cast the spell on you.
This means your party can keep bringing him back for the cost of only a spell slot. Keep in mind, though, that using raise dead comes with this cost:
The target takes a −4 penalty to all attack rolls, saving throws, and ability checks. Every time the target finishes a long rest, the penalty is reduced by 1 until it disappears.
A zealot's Divine Fury will also give you extra damage on ranged attacks while raging (which most barbarians don't get access to unless it's a thrown weapon). Once you reach Barbarian 3, then you can return to Fighter to finish out the levels (and pick up some really important ASIs to catch up).
How I would build Toddy
Half-Elf leaves much to be desired for relevant ability scores, but it lets you save a couple point-buy points that need to go to your strength. If you are willing to part with Toddy, definitely roll stats for the chance that he is super viable but at the risk that he just dies super fast. If not, use this point-buy:
\begin{array}{c|c|c|c}
Strength & \text{7 points} & 14 & \text{for Plate armor with the Half-Elf increase} \\
Dexterity & \text{9 points} & 15 & \text{18 with Half-Elf and level 4 ASI for attacks} \\
Constitution & \text{7 points} & 14 & \text{you need as much HP as you can get} \\
Intelligence & \text{0 points} & 8 & \text{hopefully a paladin can help you with these saves} \\
Wisdom & \text{0 points} & 8 & \text{hopefully a paladin can help you with these saves} \\
Charisma & \text{4 points} & 12 & \text{to use the Charisma bonus from Half-Elf (see the next section)} \\
\end{array}
Race
There is a Half-Elf variant in Sword Coast Adventurer's Guide that will come in handy called Drow Half-Elf
A half-elf of drow descent can choose the drow's Drow Magic.
This replaces Skill Versatility, but is much more useful (as your party will be better at most important skills anyway. Getting access to faerie fire is particularly useful for you as a rogue if you are the only one in the front at the time (say the paladin has stepped back to put Toddy in his aura). This is the reason we put some points into Charisma to increase the save DC.
Class
- Archery Fighting Style (this is necessary to help you hit with your attacks; and make hits with a magic stone sling extremely likely)
- Battlemaster (being able to command your allies to attack is going to greatly increase Toddy's utility)
- You want proficiency in acrobatics (to avoid grapples as best you can), perception (so that he doesn't become a tax on group perception checks), and medicine (so he can do first aid if a party member falls). Your other proficiency is up to you (although Survival would be my choice). note: remember, you get medicine and one other from your background
Equipment
- Heavy Crossbow (since we will be forgoing extra attack for a while, will replace with Longbow at level 8)
- Sling (for the magic stone spell when it can be used effectively)
- Shield, magic if possible (for those fights where Toddy is using magic stone from a sling, a tentacle rod, or dragon's breath)
- Plate armor, magic if possible (unless using the Wood Half-elf and Mask of the Wild, which is a very different build using a Breastplate)
- wand of magic missles (this gives some guaranteed damage on the particularly well-armored foes)
- wand of fireballs (this gives some burst AOE damage in fights where it's needed/useful)
- tentacle rod (for when you can safely be in 15 feet, or if you need that paladin aura so you are there anyway)
- if you don't have magic stone in your party, any magic ranged weapon will be vital (or use the tentacle rod)