My miniature dachshund likes rabbits too. I don't know if she kills them or finds them dead, but either way, she brings them up on the deck for me. (Thanks soooo much, Mimi. Nothing like dealing with rotting baby bunny to get the day off right.) And there was the time she got so excited chasing a squirrel she wound up six feet up the tree after it.
I always talked bad about the two cats and joked about getting rid of them, but they grew on me over the 15 years I had them, and I found myself just expecting to see them for months and then looking around for them....