Think the Easter bunny is the most iconic fictional rabbit? It has a lot of competition. Far from being the ultimate in non-theratening cuddly fluffiness, rabbits in movies are usually terrifying. Watch this and see what I mean. It is not for children.
Yeah, there are a few benign cinematic rabbits, like Harvey and Thumper, but the vast majority of them are murderous demons you don't want to confront, ever.