In the civilian world, usually there is no physician involved with helicopter rescue -- only paramedics or nurses.
The few times I've seen an MD or DO on a helicopter, they're an ER doc.
Now, if you're talking about the military, the flight surgeons are the ones that get to fly in the jets and helicopters. A flight surgeon is just a fancy military name for a physician that takes care of the pilots and flight crews in a unit. Usually only an internship is required to be a flight surgeon.
If you're really set on helicopters, go for the Army -- they actually have more flight surgeons than the Air Force, because of the number of helicopters the Army maintains. Otherwise, the Air Force is the way to go if you want to go up in the fighters.
Anyone else have experience they'd like to add? I might be a little off on some of my information.