I embarked with a doctor for a while, but lately I haven't bothered. Soap seems to be a more critical factor than medical skill.
As for training doctors, I've found the best solution is a "very dangerous room", that is a 4-long corridor with spike traps linked to a lever. Wooden spikes invariably do significant injuries, fairly regularly lethal. Copper or silver spears can be deflected even by cloth, and even hitting naked flesh sometimes only causes bruising, but usually against a naked target will inflict some wounds requiring medical care. If the victims are assigned a helmet and breastplate uniform (replace clothing) they should survive very well.
The reason I like the very dangerous room is that it provides a higher turnaround than 2-z drops. Most injuries can be treated quickly and the dwarf is back in the VDR for another stabbing.
The spikes could potentially be hooked up to a repeater with a cycle long enough for recovery of the wounded, that way it'd just be a matter of adding recruits to the "medical victim" squad and having that squad permanently stationed in the VDR. Oh yeah and be sure to turn it off when a real medical crisis hits
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If you think this is immoral... don't worry. The dwarves like being cared for, they get way more happy thoughts from loafing around in bed than unhappy thoughts from being injured.