I'm not advocating 4-betting QQ preflop. I'm saying you need to make a decision in your own head. Either you think QQ is good preflop (he doesn't have AA/KK) and you're going to play for it all if you catch a good flop like this one, or you think it isn't, in which case you need to fold it preflop. That's why I think any line that has "fold" in it postflop is a mistake.

I think a check raise is the best play.

If you bet and plan on calling all-in, you lose the ability to win his continuation bet when he has AK (or even AQs), but still will lose your stack when he has AA or KK. If you bet and plan on folding to a raise then you will save about $100 when he has AA or KK, but you lose the current pot and the continuation bet when he has JJ or was getting a little aggressive with AK, 88, 77, AQs, etc.

When you plan on CRAI you get the continuation bet when he has AK, AQ, or middle pairs, and you win his stack when he has JJ. Obviously you lose your stack when he has AA, KK, or TT but at this point I think the pot justifies the risk since you probably won't be drawn out on by AK or AQ...