I think it really depends on the kid.
My son killed his first with a .243 at 8. He handled it like a champ, and loved it. He had been hunting with me for several years prior, and shot guns for several years as well before I ever let him shoot at one himself. He shot the deer in my avatar at 11, with a .280 at 125yds. He just turned 13 this year and I'd take him as a hunting partner over MANY adults that I know.

My daughter is 10, and to me has not been ready yet so I have not let her shoot yet. She will probably be ready next season. I know some kids that aren't close to being ready at 12 or 13 or 14. I don't like the laws that some states have in place regarding age, I think it should really be up to the parents.