Good points all. So what if we combined the two?
The original idea was to seperate the "unique jobs" not performed by workers away from the general workforce and give slightly increased status to the person who has to perform it. Stuff like book keeping cant be done by the average dwarf. So a truly qualified doctor would be a noble and afforded higher status.
The first doctor that shows up to your fortress is a noble, but he does work as detailed above, not just sits around and changes the price of boots. Once you have him though, you can start training other doctors. You cant start from scratch with this, you need a body of knowledge in order to undestand what you are doing.
A peasant trained to be a healer can be quite competent, they will learn how to heal cuts and broken bones and to stop bleeding. But really serious injuries such as damaged organs would need the doctors attention.
So how about this:
1. The doctor noble arrives as soon as you have a decent population, maybe 50+? Upon his arrival you set up a hospital, which also functions as his office. He will often demand that you furnish it with enough beds and cabinets so that the size of the hospital matches your fortress.
2. Upon arrival, the doctor will demand an assistant, this dwarf assistant will help the doctor with all his tasks and also learn from him. In time, he would become another doctor, with equal status. They would both share the office.
The new doctor will want an assistant of his own, and the old doctor will take one as well. So for every 40-50 or so dwarves in your fortress you will have 1 fully trained doctor, and his assistant. If your population rises above 80-100, the assistant will be promoted to the rank of doctor and the noble class upon reaching the required skill.
The assistant can handle all minor and somem oderate injuries, the doctor can do everything and at a quicker rate.
But even with 2 healers per 40-50 dwarves, this would not be enough in times of war, you would want to have medics.
3. To train a medic you pick a soldier or peasant and send them to the doctor. Any dwarf will work for this but because your medics will be seeing combat it is better to pick someone with proper training.
A medic in training will tag along with the doctor much like his assistant, once he gains a competent level of skill he earns the title of medic and goes on his way.
What a medic does is a bit different from a doctor. A doctor is a civilian, a medic is a trained soldier.
Unlike civilians medics have no problem with being in or near combat. If your soldiers start taking minor or crippling injuries, the medic will run to them and patch them up, this will not fully heal the injury but it will get the soldier back into the fight.
In the case of severe injury or bleeding them medic will instead drag the wounded soldier away from combat and attempt to stabilize them and stop the bleeding. If he is successful he will head back into combat to support the other soldiers. The wounded dwarf should be far enough away from combat for civilians to come in and take him to the hospital with all speed.
In the case of organ damage or severe bleeding the wounded dwarf will instead be rushed straight to the hospital. The medic can slow the bleeding but if it is too severe then it requires the doctors attention.
4. Stretcher bearers are any dwarf assigned to remove injured dwarves from combat. You need a team of 2 dwarves for this. This is a job you can toggle on and off. If a dwarf is wounded to the point where he needs evacuation the computer picks the nearest stretcher to the fight and the 2 closest stretcher bearers.
They will head for the fight and wait for the medic or another soldier to drag the wounded dwarf into the clear.
Once the medic has done all he can for a dwarf the stretcher team will load up and rush the wounded dwarf to the hospital. Dwarves in the corridors will attempt to get out of the way of the stretcher and may suspend tasks momentarily to accomplish this.
Once they have completed delivery they will head back to combat and remain on standby. Because quick response is essential you would have to put stretcher racks around your fortress just in case.
That handles regular healers, but what about other specialists? Too many would overcomplicate the situation. In fact we probably only need a physiotherapist to help the maimed and cripple dwarves using therapy and the aformentioned prostheses.