New to this site, some of the replies here are incorrect, my guess is they are not that great at poker. You did make several mistakes there. Reraising 400 to 910 from BB is wrong. You aren't raising enough to make it definitive, thereby wasting a hand as good as QQ. Such a raise is just value-betting, and you shouldn't value-bet from BB against an opponent who's shown strength. Your read of JJ he had was wrong, but who cares if he's a donkey with A9? You can't control what other players do but you can play the right way and minimize losses while maximizing gains.
The right thing to do on his 410 reraise is to either reraise to a definitive amount(say 1400) or go all-in if you think you had him beat. You said yourself that you thought you had him beat.. so since he has position on you, why would you want to play the flop against an opponent if you had him beat? Going all-in, if he called at all, he's making a mistake unless he had AA or KK. He didn't. But MOST MOST LIKELY, going all in would've made him fold.
If you didn't like the risk, then raise to 1400 or so. You're telling him basically "you want to play with me, be prepared to lose it all", and he would've folded with A9. Then on the flop unless it's very dangerous like AK9, go all in. If it's dangerous, either slowplay and check, or slowplay then bet out a very small amount. If you did that, he would have NO IDEA WHATSOEVER what you got, and his reaction would tell you what he has. He calls, he has nothing. He reraises small, he's scared of you, he goes all in, you fold. If he doesn't go all in, then you go all in.
Your raise to 910 indicated you weren't that strong. Then on the flop you made the BIGGEST MISTAKE OF ALL. You didn't go ALL IN but bet just enough to commit to all-in. He took this as "You are weak, you are bluffing, I'm gonna go all in", and he did. Sure, he outdrew you, but you made him think that you missed the flop. That's what you want if you had AA, not QQ. He called reraise preflop so he would've had an A most likely(your read was not good), and your bet on flop made him go all in.
He may or may not be a donkey, but you made 3 crucial errors in one hand. Think about my suggestion, 98 out of 100 opponents don't ever win against me holding QQ for a reason.. I can't remember ever having someone outdraw me in your described situation because I simply don't play in a way to let them do that.