That sounds dangerous, is the dog terrierfied? Was the bullet a hollow pointer on a boxer primed shell? I believe RCBS makes a bullet retriever for just such a case. Frankly, I wouldn't hound the dog, the cartridge will probably come out in its shih tzu eventually. If the dogs poodle is greenish blue, then we know it was a copper bullet and not as dangerous as a lead one.
Gwinny, if your dog eats a 1911, you better hope it doesn't figure out how to cocker.