A 7 or 8 year old can hunt if you were to teach them to do so. An 8 year olds has conceived. So it's possible to do it at a much younger age if you have no choice.
While it may sound callous, if that 8-year-old did not produce viable offspring that could mature to reproductive age themselves, she is irrelevant to evolution. Conception is not synonymous with viable offspring.
As for the 8-year-old hunter, just how self-sufficient can they be? Procuring their own weapons, transporting their own carcasses, preparing healthy meals multiple times per day on an ongoing basis... the idea that you could just loose a 7-8 year old into the woods with a weapon and they'd survive in an ongoing sense is a bit far-fetched. Teaching someone to sneak, track, and point a gun is not the same as them being self-sufficient.