Thumper is one of the two deuteragonists (alongside Faline) of Disney's 1942 animated feature film, Bambi. He is a rabbit known and named for his habit of thumping his left hind foot.
Obviously, don't nominate any human characters. Hybrids like Cheetah or The Lizard are okay, as are shapeshifters with one set animal form (eg Professor McGonagall.)
