Alice's world is not an ordinary world. One can say this world only appears in her dream, the other can argue that this world exists in actuality on a parallel plane with the human world. Regardless, only Alice can enter this world, and she has given the world a name.
This world is called Wonderland.
The girl doesn't know how to enter the world, nor does she know how to get out. She knows if she wants to stay, she will stay, and that if she wants to return, she will return. Alice can travel back and forth between Wonderland and the real world by her will, but the gate is a secret or, perhaps, the gate does not exist. It is a paradox, a