Don't use plaster or drywall compound. Both will shrink and crack and in the case of drywall compound will take a long time to dry. Get a Patching compound. One designed for deep holes is lighter and easier to use but harder to get a smooth finish. If you use one of those patch plates you will always have a lump on the door. If you clean off the edges of the hole and get one of the patches that wedges behind the hole you will end up with a flush repair. This kind of patch may be trickier to find, but worth the effort if you are inexperienced. If you can't find a pre made one you could just make your own by wedging something inside the hole and covering the whole mess with a couple of coats of the deep hole patch and hope that no one hits the door until you get your damage deposit.
If you go looking for the pre made patch, it looks kind of like a large cocktail umbrella that you insert, expand, and then wedge against the other side of the wall (door in your case)
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