Hey vegetarians - what do you feed your dog?

I've been a vegetarian for 13 years and married a vegetarian and we have vegetarian children. I've never owned a dog. I have no moral qualms about dogs being carnivores, that's what they are. But since we bought our own house I've been aching for the dog that my parents never let me have, but the idea of welcoming dead animal flesh into our house for the first time really grosses me out, particularly the stinky stuff in the cans. I can't picture myself preparing real stuff either. Like I said, dead animal flesh - yuck. And as much as I know that it's what my dog was built to eat, it would bother me a lot to think about the many animals that died so that my dog can live. I still really want a dog though. Any suggestions?