Answer: I'm not sure if this answer will be up to your standards or not, but some character traits Alice has is that she's curious, and she's naïve.
Explanation: Alice is curious because instead of not opening the door, she looks around the room for a key when she notices the door, then she opens the door when she finds the key, and she sees the garden. A quote that show's she's curious is because when she sees the garden she says: "How she longed to get out of that dark hall, and wander about among those beds of bright flowers and those cool fountains, but she could not even get her head though the doorway," one of her main goals is to explore the area more instead of staying in the same place. The reason why she's naïve is because instead of finding a way to get into the garden, she becomes upset that she can't get in because "her head is too big to fit in the door." And instead of trying to figure out a way to get inside the garden, her first priority is to be upset because she is unable to get inside.