The only problem was that they ALWAYS laid their prize on my doorstep to show me they've been at work. It was something to come home from work and see both of them separate by 2-3 yards on the lawn laying down and moving a chipmunk or something between them....
I moved to the North Georgia mountains and something got both of them last year. I think it was a coyote, or what passes for one around here...
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.