Would you bother teaching your kid to ID an elk vs a deer if A- there are not supposed to be any elk in your area, B- there is no elk season, C-you have no reason to expect them to encounter an elk. My daughter hunts on her own. I have not taught her the difference between a whitetail and a mule deer because I don't expect her to get a shot on a mule deer in Mountain View, NC. Although she has seen enough elk that I'm sure she knows the difference.
If there is no season, and no protected status for elk she really did nothing illegal. It's a non game animal. She saw an animal that was similar to what she was expecting to be hunting. Apparently she saw it well enough to kill it with one shot too. If you are out deer hunting in an area that is only supposed to have deer, exactly what other animals have antlers?
I can't get terribly wound up about it. If the elk have become free range the wildlife dept needs to be getting the word out there. But they seem to be as surprised as the girl probably was.
FYI, the GSMNP herd has led to elk ending up in SC an GA. They like to roam and the young males have a tendency to just take a long walk.