Doctors aren't a vital part of space operations, really.
Yes they are - the Flight Surgeon position is an essential part of the ground control on 'real' space missions.
(Alternatively, medical professionals are also an essential part of modern naval crews.)
Some off-hand references:
* Dr. Khalsa, on the Tiger's Claw (Performed Ralgha's trank-chem debriefing.)
* The TCS Austin had a full-fledged psych ward.
* Spirit's fiancee was a fighter pilot assigned to the 'Medical Corps' at Epsilon Station.
* There was a Drayman hospital ship in the Dakota series.
* The Amadeus in the WCIV intro had the Red Cross logo.
* There was a WCA episode in which the doctor and nurses onboard a hospital ship (TCS Pleiku) played a huge role.
* Doctors treat people at various times in End Run/Fleet Action: Svetlana had brain surgery at some point, landing craft at Vukar Tag did medical evacuations, a corpsman treated Big Duke after the JCS bombing...