In a situation where you are close to the final table you should only raise with hands you are willing to call all in with. If you don't want to push all in with QQ, then my advise would of been to limp preflop and see the flop. With so many players limping and the blinds and antes being fairly high, it's going to take a fairly large raise to push out players with AK, AQ, AJ, AT. All of those hands are a possibility seeing as you are going to be playing short handed with 11 players left.

In this case that you present, we are missing too much information to make a good decision. To make a proper decision we need to know: How many chips you have, what are the blinds and antes, how big did you raise, how big is the push, what are the stacks of the 2 remaining players, and what are the stack sizes of the blinds (who are out of this hand).

With the limited information I would call the push. You can put the 3 players on a range of face cards. I would expect to see two, if not 3, of the A's used in hands. That leaves the player that pushed chasing 1 or 2 outs if they have an A. You already have a made hand and are hoping for 2 outs to improve your hand. The only two hands that have you at a disadvantage are AA and KK.