Sometimes dogs and cats will eat dead things they find ... but mostly they just carry them around, chew on them and roll on them. I would be a little concerned though, about your dog becoming infected with internal parasites from the dead rabbit. You might wish to ask your vet if he/she thinks a stool sample would be prudent at some point.

As for dogs and cats killing rabbits and mice ... you know ... dogs and cats are predators. Mice and rabbits are prey. That's the way the world is. I don't like it when my dogs kill a rodent or rabbit or bird ... especially if they bring it in the house and I have to clean it up. Bleck. But I don't blame them for it, they are doing what comes naturally to them. It is their instinct to kill. If one chooses to own a cat or dog, knowing that they are predators with a prey drive and are going to kill something someday is part of the bargain. It's really not wise to own a predator if you absolutely can't deal with death.

Having both predators and prey in the same household is risky business. Sometimes nothing goes wrong for years and years ... but once in a while, some little critter dies. That's the chance you take when you choose to own both predator and prey.