Strictly speaking, this one isn't a zoo joke - I could have re-written it as such, but thought it worked better just the way it was as a general veterinarian joke.
Well, the vet looks at the dog and instantly realizes... it's dead. Just to be thorough, he checks its breathing (none), takes its temperature (cold), and feels for a heartbeat (none). Sadly, he shakes his head and says, "I'm sorry sir... your dog is dead."
"No, he can't be!" the man exclaims, "There has to be another test or something!"
Sighing, the vet leaves the room, only to return a few seconds later with a kitten in his hand. He places the kitten next to the dog. The kitten sniffs the dog's body for a moment, then turns back to the vet, mewling pitifully and shaking its head.
"That doesn't prove anything!" exclaims the dog's owner.
The vet picks up the kitten and leaves the room again, returning moments later with a golden lab on a leash. The (live) dog sniffs the dead one for a second, then whimpers sadly to the vet.
By now, the dog's owner has come to accept that his pet is, in fact, dead. With a heavy heart, he scoops up his dog and starts to walk towards the exit. It's then that the vet coughs slightly before mentioning the bill.
"What!" balks the man. "You didn't even do anything!"
"Ah, if only that were true," replies the vet. "If you'd just taken my word from the start, it would have been free, but with the cat scan and the lab test, it comes out to $500."