In general the DC of abilities of keyed of HD, however, the pixie, being a 1HD creature can give up this HD when taking class levels.
So how are the DCs calculated in this case?
The rules are inconsistent.
Different parts of the rules give different formulas for the DC of supernatural abilities.
The section on reading monster entries says:
When a special ability allows a saving throw, the kind of save and the save DC is noted in the descriptive text. Most saving throws against special abilities have DCs calculated as follows:
10 + ½ the attacker’s racial Hit Dice + the relevant ability modifier.
This matches the DCs given in most published monsters' stat blocks.
Meanwhile, the section on supernatural abilities and the Rules Compendium (p. 119) give the formula as:
10 + ½ the creature’s HD + the creature’s ability modifier (usually Charisma).
I don't know of any official resolution for this discrepancy; ask your DM which formula is being used in your game.