I had Tirai in the resort so I could try out the Battle Quests, when she wasn't able to even after being full/happy, I took he rout and tried again. Still nothing.

Do they have full HP? Are they stuck in a battle? Is this pet from a transfer?

Just wondering some of those often are factors as to why pets cannot battle. [edit] Your pet needs to be healed in order to battle. :D

Oh, thank you! She had 0HP