Well, to unlock the unmarked door at the room of the princess, you will need to catch 8 shiny rabbits. To make them appear, speak to Toad at the princess' Rec'room. Then some of the rabbits (about 1/15 of them) will be white and shiny. I would recommend Yoshi for this trick 'cause he has 6 rabbits at a place (outside the castle), and he can catch them easily. After you have caught 8 of them, the unmarked door will open, allowing you to take its content : a Power Star!