Hiring a new doctor with a higher level after the injury will speed up the time of the recovery, but only by a small amount.
The doctor also heals your player faster since the new staff system. So a higher level doctor surely pays of. However the most important part of the doctor is still making sure the player won't get injured.
BTW... I'm THE wizard... not A wizard.The difference being pie. The wizard gets free pie. A wizard gets nothing.