Mackenzie is extremely rare over here. It's only used as a last name.
Molly isn't Irish either :)
Some Irish names
SineadRoisinAineLaoiseAilisAisling (which I think is perfect for a princess as it is often used in poems for a princess. It means "dream" or "vision")
AoibheannAoifeMeabhNeasaMaireAssumptaBeibhinnBrigidCaitlinCaitriaCaitrionaEabhaTreasaSorchaSaoirseCliodhnaDearbhailEilisEithneOrfhlaith (which is also good as it means "golden princess")
EmerEireannFeidhelmGrainne
Also for more names go to here:
http://www.behindthename.com/nmc/iri.php