The effect of the doctor is to reduce the length of injuries (or at least the percentage of injuries that are long term), rather than to make them heal faster after they occur. A top level doctor will convert many injuries to the length of the game only, and the player will be healthy for the next game.
Finances in D.IV are pretty tight, so I'd spend more on the trainer, then the doctor, and finally the PR guy. But I'd probably keep it around the 4-6 level for a doctor.
The staff system is going to be revised during this season. I don't know whether there will be any advantage to hiring a doctor now, or waiting until the new system is in place.