A Boni Giant Sengi
The animal that is constantly disappearing in Alice in Wonderland is the Cheshire cat. He can fade in and out of sight at will.
The Walrus
jabberwocky
The Jaberwockyand the Bersnach
the big fat cat
The Cheshire Cat from "Alice's Adventures in Wonderland" by Lewis Carroll.
Most of the citizens of Wonderland are animals, so almost any animal costume should be appropriate. Many of the animals wear clothes, in a Victorian style, so a Victorian type outfit with an animal head or mask would also be good. The other large group of 'people' in Wonderland are playing cards. Two large pieces of card depicting the front and back of a playing card, joined at the top so they can hang on the shoulders would be very Wonderlandish. There is also nobility living in Wonderland. You might like to be a prince/ss or a baron/ess or something similar. In Tenniel's drawings, the nobility wears Tudor style dress, to match the style of the royal playing cards. And there are also servants, who dress in a Victorian style. If you also wish to draw inspiration from Through the Looking Glass, you could be a chess piece, a talking flower or a character from a nursery rhyme. Failing any of that, you could go for the old reliable blue dress.
The character
Looking through a microscope, most animal cells are pretty much entirely transparent unless you dye them.
In 'Through the Looking Glass' the Lion and the Unicorn did battle and the unicorn pierced the Lion through his heart.
Napoleon is the anti-hero of the book Animal Farm. His character is a metaphor for Stalin and the anti-hero gains fame through selfish means.
The major character in "Animal Farm" is a pig named Napoleon.