Dude, death is not a difficult subject. You shoot it, it dies, and doesn't come back. If a gorilla can understand death, I am sure an 11 or 12 year old could, especially when they've been hunting. And kids aren't as stupid as you are making them out to be. I was programming computer games at the age of 12.
Lucky you're not the one on trial for murder right?
Also it's funny that you're implying computer programming anywhere near as complex a subject as death, and indeed murder (it's motivations etc) is.
It makes absolutely no sense to judge the kid as having the same brain that you, an advlt (or at least someone in their late teens, I'd hope) has. Think about all the things you can do now you couldn't as a kid, as well as all the things you understand a lot better, like having empathy with people, not being selfish, social skills and so on. Understanding of death is something that only comes with age, and shooting a few rabbits isn't going to hammer that home when you've got a young kid involved. All it does is teach them that they're praised when they do do it.