DISCLAIMER: I'm not too interested in Alice and the Wonderland so something I may be confused about might be common knowledge.
I can't say much about the protagonist. I can tell you she's a Brit since she used the word "muddle" and it seems like she's adventurous since we don't see her crying about her current situation. If anything, we can have a glimpse into her head once in a while to see how she's dealing with all of this.
Also, I noticed is that her name went from Adelaide to Alice when people in this world were referring to her. Was that name change on purpose?
I believe the story is going to lea us to why she was brought to Wonderland. I bet there's a reason why she was brought there but it's up to her (AKA us) to figure that out!