How Long Will It Take for my Indented Facial Scar to Heal?

I had skin cancer cut out of my upper lip approx 9 months ago which has left an indented scar running straight down from under my nose to my upper lip. Alot of doctors have said that the surgeon has done a wonderful job and it is a fantastic cut but I'm unhappy that it is indented. My surgeon said it will even out and heal by itself completely between 12 and 18 months do you think that can happen since its already been 9 months and little has changed? Should I wait or have a dermal filler now?