[pushkins]

From what you are describing it sounds to me like a simple replacement of the door trim.
Buy a piece of door moulding that is the same mould, measure and cut the 45 degree at the top and nail it into place. Once you have done that you can simply use wood putty to fill or repair any other damage "rover" did to the frame, finish with a small amount of caulking if needed then paint.
Unless the sheetrock is chewed back past what the trim covers don't worry about it.

On a scale of 1 - 10 (10 being hardest) it's a 3 with about 30 minutes in work time.