This is safe and a common practice. POE is extra-low voltage (less then 50v), so there is little risk of shock or fire. The risks are more around cable non-performance/signal loss.
In many (I expect most) countries you can legally do this work yourself (In New Zealand we can, Aussies are not supposed to - that seems to be a union/labour protection thing to me)
There are lots of "gotchas" if you are worried about getting the cabling to spec - and if you need to ask you likely won't get it to spec. The cables will still work but may have a bit more signal loss. If you want perfect, you need to do a lot if reading/studying or engage someone qualified - but in practice it will normally be just fine if you terminate both ends properly.
Some easyish best practices -
- Solid core in walls, multistrand for patch leads.
- Total length including leads less then 100m (I think less then 80m in walls)
- Separate data and power by at least 2inches/50mm. Cross power lines at 90 degrees.
- Dont bend cable to sharply (at least 8 times diameter of cable bend radius)
*Pay attention to cable termination - this is where most problems occur. Google TIA-568