Yes, there is a type of doctor who travels. These doctors are known as locum tenens physicians and they provide medical services to hospitals, clinics, and other healthcare facilities on a temporary basis.
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A doctor may not always be seated in the cabin on your flight, but most commercial airlines are aware that in-flight medical emergencies can happen (I've written about one or two such instances myself in my time at USA TODAY). Most carriers contract with on-the-ground experts in emergency medicine at altitude.
A trained physician is aboard just about 11 of every 12 flights. The New England Journal of Medicine discovered that in-flight medical emergencies are rare to begin with.