...I really believe that kids should demonstrate some responsibility and drive before arming them and bringing them into the woods.
You're a good dad. Hunting needs more fathers like you.
Anyway, here's an idea for a youth deer gun: Marlin 1894C. Lots of hunters knock deer over with 'em. They're small, have virtually no recoil (my very petite wife, who hates recoil and won't shoot a 30-30, doesn't even notice the .357).
Plus (I've said it a lot, and will say it again), they're so darned cute!