My seven year old is going for deer this year with a Ruger compact 6.8 fitted with a Leupold 1-4. I traded into it when he was a toddler with just this purpose in mind. He's been making his own (very supervised) handloads and we're both pretty pumped.
The AR is a good option with the adjustable stock but I want him to have a good foundation with bolt actions since he'll likely use them more often in life.
For anyone interested, I'd highly recommend the bog pod tripod for kids. My son is deadly with them.
