I think this is a Crosman Airgun (Desert Rose Lever Action BB Gun). I hope it is, although it doesn’t really make this any better.
I wouldn’t let my kid fire any type of weapon while my dog was in front of her, even if he is off to the side. You never know what the kid is going to do or where the dog is going to run.
Know your target and beyond is a basic principle of safe firearm usage. And teaching your kid that “sometimes” it is okay not to follow the rules is just asking for trouble in the long run.
Make a safe field of fire and put some targets up for the kid. And keep the dog inside while you are shooting, or at least put it on a leash and keep it behind the line of fire.
