What to do with Pocket Queens when reraised preflop

I had pocket queens and reraised an UTG raise and then got reraised preflop. It was the beginning of the tournament with full 30000 stacks. I am always worried about pocket AA or KK preflop when having Queens.  I called the bet and thought Villan might have AK also. Then the flop came paired with 6s and a 4.  Villan bet 11000.  I thought if I was good preflop I would be good now and thought about going all-in but ultimately folded. Villan turned over AK suited and said they would have folded to my all-in.  How do you play Pocket QQ when reraised after you 3-bet preflop especially when stacks are deep at the beginning of tournament?