QQ is a great drawing hand, great heads up, and in the elite category of hands.
Raise it 3-5x the bb (exception is when the blinds are low like 10/20, then I usually raise it a little more).
If an ace or king hits, make a bet of 1/4-1/2 the pot, not all your opponents play every ace they get to a raise, or king for that matter. If you get raised, its an easy fold. If you get called, beware. Often enough, you will get it folded to you.
If an ace or king doesn't hit, and you have an overpair, feel pretty confident about it, but look out for possible sets, alot of people like to play small pairs, and I have lost many qq, kk, or aa overpair hands to a set hitting on the flop.
I usually bet the pot if no a or k hits, make them draw to their 3 or 6 outer, and if they do have a set, they usually raise there. Then its up to you to decide if you are against a set, or just against top pair.