I would probably lead bet the flop, but turn it into a bet/fold because with those two big overcards, you have 2 outs to another Q, while there are 6 outs to an Ace or King. Given the aggressiveness of the other players, sometimes you just have to fold an unfortunate strong hand on a killer flop and live for another hand.

Yes, a Jack came on the turn giving you 4 more outs, but you wouldn't have been thinking that before hand.

Your action preflop was good, but bet the flop and fold on a raise.