Dogs are naturally programmed to hunt other animals. Killing is a natural behavior and when dogs don’t kill it’s only because of human involvement. The fuzzy squirrels and sneaky raccoons your dog loves to hunt however, can carry harmful disease. When your dog has killed or eaten an animal you should be concerned when the animal is illegal to hunt with a dog or if the animal carries harmful substances.
Eating a wild animal can be harmful to your dog dead or alive. Dead rats or mice will commonly have poison in them. It is also possible small mammals could be carrying fleas, which can be transmitted to a dog or cat who encounters them. Take your dog to the vet for x-rays as soon as you can. Inducing vomiting could harm your pet if bones cut the esophagus. The X-rays will reveal if any bones are dangerous to internal organ if left to pass naturally. If this is the case then the vet will need to perform surgery to remove the bones. If the animal eaten had ingested poison it could also be passed on to your pet, just like a contagious worm or virus. When you take your pet to the vet make sure they check for anything harmful your pet may have inadvertently contracted. Also, always inquire about worm, flea and tick prevention products and protocol recommendations. There are some very good products available, and they are very easy to administer yourself.
In the US, the Fish and Wildlife service regulate hunting restrictions on dogs. Dogs may not be used in hunting bear, deer, elk, antelope and turkey. If you are outside of the specific hunting season for that animal, your dog absolutely cannot hunt for it.