An interesting word not because of the Bunny Suicides or Knuffle Bunny or Pat the Bunny. None of these.
Interesting because the etymology of this one, at least OED-wise, is unknown. I would guess that it ranks among the most commonly spoken words among American children--but how it came to be? Tonight I have no idea. It has something to do with bun, but that's where the question mark begins. Bun does refer to the tail of a hare but that still doesn't suffice.
Sometimes I want answers more than I want to sit with questions; this situation is an example of one in which I like the question--how did the word bunny come to be?--in and of itself, whether or not I find the answer.