Maybe this is the right place to post this? We have several dogs and when they were younger, they scratched our doors. I'd like to try to fix this so my current plan was to take the door of it's hinges, fill in the gouges and scratches with wood putty, then sand it down first with an orbital sander and then by hand. And then try to match the stain.

My questions are: does this sound like a good process for fixing the door? Am I missing anything? I'm actually not sure whether this is just a stain or sealant. How can I tell and which is best for an internal residential door? How do you color match such things?
Many thanks in advance.