I have a 6 YO daughter, in about 3 weeks I will be picking up her first .22LR. A Henry Mini Bolt Youth. Try as I might, I just can not quite imagine her squeezing one off on a center fire bigger than a .223!
To put it in perspective, I am the "child" who got all of the Want-To-Shoot in the family, but not a whole lot of the natural skill. My sister is 18 years younger than I am. When she turned 11, I got her a .308 savage with a muzzle brake. I loaded it down with H4895 as listed on Hodgdons website. But at age 6, she was still shooting .22LR. I think she was about 9yrs. old when I let her squeeze one off with a .221 Fireball I had at the time. Man I miss that old .221.
I had to learn the hard way, my sister on the other hand can flat out Shoot! She took after our mom, who up untill shortly before her death, could still handily out shoot me with pretty much any type of firearm. She never taught us kids though.. It was not until I started taking my sister out to shoot, that she occasionally would tag along. /shrug Probably TMI, sorry
Hope I did not come off preachy! Definitely not trying to tell you what's best for your child! It is all about going out and having a great family outing for me and my daughter. Heck, even my wife is finally beginning to show some interest in learning to shoot! Good times ahead. Can't wait for her to get her youth .22lr, so she don't have to try to deal with my full size .22lr, which is very awkward for her.
By the way, a well thought out .223 load can reach out to 800++ for target shooting purposes, and can carry pretty decent energy out to 200 well enough. Not sure about legality of hunting with it in the various states. I live in CA...