I do see how the White Rabbit as Virgo would fit, too, now that you mention that. I don't know much about personality traits associated with zodiac signs. I only know some of the stories, like that Virgo is supposed to be the goddess of justice. But I do think White Rabbit fits as Virgo/the virgin. The coloring of his fur is symbolic enough as it is.
Yes, Alice Liddell is who Dodgson wrote the stories for. =) At the end of Through the Looking-Glass, there is even an acrostic poem which spells out her name. Apparently, she was kind of like a goddaughter to Dodgson and they kept in touch with letters and such. Some few years after the publication of the first book, Alice stopped replying to his letters, though (she had grown up, gotten married, etc.), and then he wrote the second book. In my opinion, it has a bit more of a darker/melancholy tone, but that could just be me projecting other ideas onto the story.