You can buy a ticket for anyone with your miles, you just can't combine miles with someone to purchase a ticket. So yes, you can do that.

Just book the ticket online and don't indicate he's a minor. Even if you fill out the birthdate on the traveler ID part online, it still won't matter. I do this all the time, I book my kids' tickets as adult because it makes no difference so far as I can tell in fare or anything and helps avoid any unnecessary hassles.