I always found it really interesting that Alice goes to other worlds in two different ways. In the first book, Alice’s Adventures in Wonderland, she follows a white rabbit down a rabbit hole. In Through the Looking Glass, she steps through a mirror into the world mirroring her own. The way I see it, her methods follow her growth.
In Alice’s Adventures in Wonderland, Alice, tired of watching her sister read a book with no pictures, follows a strange rabbit down a rabbit hole, and discovers Wonderland. In Wonderland, she is constantly changing size, and can never seem to figure out how she is supposed to be. This is similar to the feelings we attribute to puberty. First, there is a fascination with the world around you, as you are now old enough to explore it a bit on your own. This is why Alice follows the rabbit; she is curious about the world around her. Her size changes while she is in Wonderland mimic the changes one goes through during puberty, when one barely recognizes oneself anymore, because they are changing so fast.
In Through the Looking Glass, Alice goes through a mirror, because she is curious about the world on the other side. The mirror is important, because in it, Alice would see a reflection of herself. Now that she is older, she is curious about herself. We also see signs of her being older when she chastises the black kitten for being unruly. Likewise, Dinah has grown up and become a mother. Alice’s quest to become a queen also shows us that she has grown up, but her lack of confidence in ruling also shows us that she is not all the way grown up yet.
My only problem with this analysis is that, in Through the Looking Glass, Alice is only 7 (and 6 months). Is it just that the Victorians have a drastically different conception of when one became an adult, or is there something else going on here?