The implication is that the virus worked VERY fast to kill off humanity because no one apparently even had time to raid stores for provisions. As for where the bodies are, I think it's a budget issue. Cheaper to not litter every scene with rotting corpses and skeletons. And this is a major network comedy, so littering scenes with corpses might have been a bit too dark. "LOL, Phil is having trouble getting those bodies into a mass grave!!!"
As for animals, no clue. Phil and Carol are now talking about gardening, but there is no mention of hunting. And no wild animals scavenging the towns with Phil. No mention of Phil carrying a gun for protection from possible wild animals (just for fun).
Maybe this super virus killed off (almost) every complex organism on the planet?