Think "pre-flop"
I think the answer to your question lies in the pre-flop play. U got a 3bet raise by some mid-pos, and as any of us would do with QQ in the button, you re-raised 3times. But then again your bet was called by the BB, which couldn't call a 9bet in that pos with just (A)high, so it has to/could be a pocket pair. The bad luck is that the nor flop nor the turn, produced a card higher than your pocket QQ's. Plus the BB checked, and a higher pair than what the flop produced, will raise there. I assume you wanted to fold him because you thought he had a draw, but the pre-flop call wouldn't indicate (to me at least) that he called a 9bet from BB with QJ or 78. Best thing to do there is make a small bet on the flop, see how he reacts. Usually, set holders respond with aggression to small bets because they want you to go allin and he checked in order to mislead you (which is something we would all do). His intuition most likely
tells him your holding a pocket pair as well. A re-raise from him in this case, could also indicate a
bluff, or you could just put him on AT, but the pre-flop play kinda eliminates those 2 options. Then again it's hard to fold the queens, especially on that turn and you holding an overpair. But you made a pretty big raise and he put you allin. That early in a tournament (especially bounty builders), you don't go allin unless your 99% sure you have a winning hand (not that things couldn't change on the river). As a matter of gameplay, the set holder played it perfectly and he baited you (which you fell for). Any A or K would have made you think twice about calling, but none came out. Still, it's the allin that should have tipped you. The amount you raised indicated you were prepared to pay it, and the re-raise should have told you that the opponent has no fear of whatever chips you have left. The turn, was definitely a fold after the re-raise. Checking the flop could have resulted in you seeing the opponents hand, but its very unlikely. He would have went allin on the river. Man... there are really so many ways you can think of this hand, and you can plot a good play and/or bluff, but all the science in the world, can't help you against luck. We've all been there.