Once in the Fairy Resistance HQ, speak to the Fairy Queen, to start the quest. If you have just finished completing Fairy Tale II - Cure a Queen, you will have to wait around thirty minutes in order to begin this quest. If that didn't work then logout and login again, and then it should work. Talk to the Tooth Fairy and she will ask you to turn on the projector to watch a briefing about Fairy Tooth Magic.