How did the word "bunny" come from "rabbit"?

When I got back from India, I discovered that my sister had a new bunny. Her name is Chloe, a.k.a. Batman. Our dog, Minthil, has been very jealous of the attention that Chloe/Batman gets, but then she relented and just became incredibly curious about this strange animal that is small and fluffy, but isn't a puppy. Minthil's confused expression means: "Why doesn't she like it when I play with her?" Our answer: "Dogs may like chasing and biting, but rabbits aren't so fond of that game." Fortunately, Minthil has calmed down and now she just tries to lick Chloe... don't ask me why.

This is a video of Minthil trying to get at Chloe, while sitting in my lap - very awkward for me.