I would mostly be worried about internal parasites, specifically worms, when it comes to our animals killing outside critters such as bunnies and squirrels. I live in an area where hookworm is a huge problem, so I have a fecal float done every time we go in for a vet checkup and worm when/if needed.
I am not so much worried about my cats because they operate a great catch-and-release program with the field mice that like coming into our house around this time of year, but I do worry about the dog who is the most likely to kill something. I do, however, hunt rabbit to feed the dog, and I freeze those for at least three weeks before feeding them to make sure parasites they might be carrying are dead.
Even with freezing the rabbit first, I hope you are cooking it before giving it to your dog.
I learned a lot about parasites and freezing wild game & fish from doing my own smoked jerkeys & smoked fish.
When I started out, full knowing there might be food safety issues if not done right, and not properly researched, I spent considerable amount of time making sure I was doing things properly to avoid getting myself, friends or family sick or infected with parasites. Here is a bit of information I learned. This topic also comes into play with sushi, noting almost ALL fish have parasitic worms.
Sushi Grade fish is frozen before shipping to Sushi restaurants in a special commercial grade freezer that gets WAAAAY Colder than a residential freezer does.
Trichinella parasites in wild-animal meat are not killed by freezing, even over a long period.
Freezing wild animal meats may not effectively kill all worms because some worm species that infect wild animals are freeze-resistant.
A temperature of -31 F (-35C) is required to kill tapeworm eggs and larvae, as well as other parasitic worms.
Home freezing cannot be relied upon to destroy these.
Hence, it is not safe to feed your dog raw rabbit or any raw meat that has been in your home freezer, even for 3 weeks. Not even for 3 years.
If you want to feed it to your dog, proper COOKING Temperature, not Freezing temperature is the real key to safely avoid parasite infestations.