I have something similar. But in better shape. It's a break open, single action pistol. On the handle is engraved a rabbit on one side and a deer on the other. My dad had it since he was a kid. Passed it down to me. He claimed to be able to shoot it. I'm in the same boat as you. No info.
Is there a little notch in the end of the barrel, right where the hammer falls? If so, I remember
seeing these years ago, sold as keychain trinkets. 2mm pinfire, and they would shoot a
(I think) #6 lead shot.