My youngest son killed a doe last year with a nef .223. He now shoots a 7mm-08. The single shot 243 kicks harder than the 7mm-08. I also would say get him a good scope. But I'm not talking about a high dollar scope. Look at the bushnell banner 3-9x40 with 6 inches of eye relief. Nothing scares a kid more than having a scope pop em. Some times once is all it takes.
My son weighs <60 pounds and shoots a .308 with Remington managed recoil ammo. I have that Bushnell long eye-relief scope on my son's rifle and his 20 ga slug gun (and I have one on my slug gun). It may not have the best glass, but it does the trick and will keep the scope off of your nose, eyebrow, and forehead.