QQ is one of the few hands I'll often call a 3bet oop with so I don't mind the call pre - against this kind of player, you probably can't profitably 4bet since he probably doesn't have a 3bet-fold range, so when he 5bets you'll have to fold.
If there are any overcards on the flop, and indeed even if there aren't, you're in a tricky spot against someone playing 12/12.
Perhaps it's better just to fold preflop - it seems really weak tight, but I dunno, I'd generally call here, and often get myself in trouble.
EDIT: I just noticed he's only like 30bb deep - I might well just 4bet and get it in here, it seems kind of odd for a 12/12 to be sitting short like that but meh, I don't really know if I could find a fold vs someone 30bb deep with a hand as strong as QQ, I guess it depends on his 3bet range, if he's only 3betting {AK, KK, AA} then you've got to fold, but vs say {QQ, KK, AA, AK, AQ} you've got enough equity to get it in and be no worse than flipping against that range.
Bearing that in mind, and that he's 12/12, although it's a tough one, I think perhaps folding is best. If he does 3bet wide enough that you have some fold equity against the weaker parts of his range, that probably doesn't compensate for the times he 5bets and you have to fold having put a ton of dead money in the pot.
If he was 100bb deep and the sort to only 3bet hands he'll then stack off with on the flop, you could call to setmine.
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