If a police dog is considered a police officer, why they don’t need a search warrant for a dog to search a vehicle on a traffic stop?

This is an EXCELLENT question. The evidence of a dog's scent is permitted under the doctrine of the plain view exception. The first case on this held that a policeman seeing evidence of crime through the window of a car or a home removes the warrant requirement of the constitution. The reasoning behind this is the expectation of privacy, if incriminating evidence is hidden from view, the shade is down or its under a blanket, a warrant to search is required because you have an expectation of privacy because what you are doing is NOT in plain sight. So the dog situation is under the plain view exception because the dog can smell what is in the air, in plain view of their nose so to speak. But if they have to bring the dog into your home or car to make the discovery, then a warrant is needed.   Best of luck to you and I hope that you never have this area of law affecting your life.