Great story, but I'm wondering about the legalities in that State ---age, parental supervision, whatnot.
I also wonder if a sporter in .308 was the best choice.
I 'spect the idea of "taking him on a hunting trip," rather than actually "hunting" was the real idea.
Age - Most states merely require adult supervision(not specifically parental) along with the kid. Rules vary somewhat, but generally require that said adult actually be with the kid and able to practice some control over him or her. Line of sight/earshot type stuff. Most allow or even require the adult be hunting as well(IE have his own license/hunting permit/tag), along with a weapon.
For that matter, a 'youth permit' attached to the sheriff's might not take into account that the kid isn't a resident of the state.
Beyond that it can get funky - some states would require that the kid take at least the first shot for it to go onto his tag (after that the animal is assumed to be wounded and anybody can finish it off), some allow any tag in the 'party' to be used on any animal. IE Pops can take his wife, gramps and grandma out 'hunting', and get 4 deer without the other three ever so much as firing a shot.
A sporter in .308 might be a touch heavy for the kid, but he would, even theoretically, only need to make ONE shot with it, after that the sheriff could administer the coup-d-grace.