Though remember, there has to reasonable belief of death or serious bodily injury to a human being.
In and of itself, the fear that someone may kill your dog has no more legal significance than someone pointing a gun at a lamp. This would be particulaly important if your dog is a chihauhua or you're talking about a cat because you would have to argue the threat of hurting your pet was an act by the intruder in an attempt to remove a roadblock to shooting YOU or your family. Unfortunately, you simply can rest your legal argument on it's laurels simply because the man was in the four walls of your home.