first hand QQ, what to do when you have no read on opponent

[AACardPlayer]

So these kind of hands trouble me somewhat. Not because I lose most of them (maybe I've already answered my own question before I even asked it) but because I just don't really know what to do. I usually play $30+3 on party, finish in the money 37% (don't know my ROI), but my bankroll is ever so slowly increasing, so at least it's positive.

Enough with background info, to my problem:

1st hand Party 30+3 Sitn'Go.
Blinds 10-15. Everyone got 800 chips.
I get QQ in cutoff, two limpers, I raise to 85.
SB makes it 200, BB folds, limpers fold.
What's my play here?
If I call and the flop comes out rags with my QQ being an overpair what's my move if he bets half-pot, pot, all-in, or checks?

1010 I can usually lay down pre-flop here, JJ maybe, but QQ?
In later rounds, when blinds are higher, I have little to no choice but to go with my hand but when the blinds are still relatively small?

Thanks in advance...