As you have likely read, as of next release Dwarves will soon be able to stem bleeding with bandages and do other things to wounded dwarves. In addition, there is currently already a problem in that military dwarves entering a combat will focus on fighting, while non-military dwarves will run away; there is no way to tell a dwarf to drag the wounded out of combat! Compounding this there is the difficulty that even if a wounded dwarf is not near active combat, orders telling non-military dwarves to stay inside can still prevent him from getting help.
With the addition of medical skills and a hospital, this would be a perfect time to add a labor or a military role of combat medic; a dwarf that will enter combat only to go to wounded dwarves, perform first aid and bandaging if necessary, and carry them to the hospital or barracks. Having the fortress physician doing such rescues by default would make him far too likely to wind up killed. Having all military dwarves do rescues would spread medical skills too thinly among them. If they just carry fellows back to a physician for treatment it could work, but that presents the problem of your champion carrying wounded dwarves inside the fortress when he should be out in the field fighting.
All that considered, it seems the best solution is a special military role where the dwarf assigned would grab injured, non-ambulatory dwarves, patch them up on the field if necessary, and haul them to the hospital or barracks while ignoring foes and not engaging in combat.
Thoughts?