You can repair a wood door about the same way that you repair a hole in drywall except using an epoxy like Bondo or Minwax High Performance Wood Filler. That said, and since you will have to refinish the old door because of the hole, my feeling is that you are about as well off to replace the door. You can get a door only, without the casing, pretty cheaply at a home center. Then you just have to copy hinge and door handle locations and holes onto the new door and refinish. It will be difficult to refinish the old door because of blending the hole repair into the rest of the door but you do not have this to consider with a new door.
Henry in MI