[BotOnTilt]

QQ is an annoying hand to have when you get re-raised. It was probably one of the most expensive lessons I learned when I started, I was always eager getting it in on low flops with QQ against PF 3-bettor thinking he might have JJ or bluffing with AK. But I don't remember villain ever having a worse hand than I did.

You have no reads on villain? This is basicaly one of those spots where you really have to make the decisions PF IMO. Its true that you can play for set value since his raise is not that large to the stacks (120BB deep).

If he was very loose and aggressive I'd 4-bet him PF, otherwise you should have bet flop to find out if he has AK or a higher pair. The thing is that most players have a very tight 3-bet range at NL5. I think its very rare to get 3-bet with JJ or worse (if villain is a maniac then its different). But against an unknown its likely you are up against AK or KK+. Betting the flop would have allowed AK to fold/call or KK+ to raise. By check-calling you found out nothing and are essentially committed. If you are confident that you're ahead of his range you can CRAI if not then you made a mistake before the turn.