QQ in BB late in tourney after 3 all-ins

[OneByPhi]

Live $25 NLHE tournament. 28 players started, 10 left. This is the first hand at the final table, and the other 3 players involved were not at the table I was moved from, so I have no reads on any of them. Stacks range from 7,000 to 32,000, but most are 10-15,000. Blinds are at 1,000 and 2,000.

UTG goes all-in for his last 7,000, 2 folds, the next player thinks for a few seconds and then goes all-in for his last 8,000, folded to big stack in SB who instantly pushes all 32,000 of his chips in. I have 9,000 left after posting by BB, and I look down to see Q [img]/images/graemlins/spade.gif[/img]Q [img]/images/graemlins/club.gif[/img]. My first impulse is to push, but I am trying to improve my game by resisting impulsive play and actually thinking through situations like these.

I reason that UTG is about to be eaten up by the blinds, and if he is savvy at all, he could have made his move with almost anything. Similarly, the next player is under pressure, but since he called instead of acted first, he probably has some kind of hand, even if not as good as my queens. The big stack worries me. He insta-pushed, which he may have done just because he was big stack and it only cost him 7,000 to contest a pot with 18,000 already in it, and he may have reasoned that his move would make me fold, and even if I called, it would only cost him 3,000 more (11,000 total) to see a 37,000-chip monster pot. Even if he lost, he'd have 24,000 if I folded and he lost to one of the short stacks, and 21,000 if I called and he lost to me. I figured that he probably has at least a fairly decent hand (maybe a middle pocket pair or an A with a solid kicker) but since I don't know him, I really have no idea what to put him on.

With no info on the other players, it was hard to put them on hands, but I figured something like KT for UTG, A9 for the first caller and 88 for SB might be reasonable, although they could easily be either much stronger or much weaker than that. I didn't know the exact odds, but I figured I was probably about 40% to win against that group of hands (I ran QQ against those hands when I got home, and oddly enough my guess turned out to be almost exactly the right odds if they had held those hands). I knew that if any of them had AA or KK, I was in huge trouble, but I figured that was pretty unlikely, so the question was, did I want to play for my tournament life there as the probable favorite, but likely less than a 50% chance to win. If I called and won, I would be chip leader, but if I called and lost, I would be done. If I folded, I would be down to 9,000, and in the SB in the next hand.

What would you have done, and why?