[Moneyline]

I'd bet the flop here. There really is no way to protect your hand on the flop. If you go for a check/raise you definitely won't protect your hand if either no one bets or the player on your left bets.

If the player in MP bets, that doesn't do you a whole lot of good either because the only person a check/raise will potentially squeeze out is the EP player. Furthermore, the only hands a check/raise will likely drive EP out with are hands like gutshots, middle pair or bottom pair. And you're not even guaranteed to drive him out if he holds one of these hands if lp player calls MPs bet. Then the pot is so big that EP may very well call and not make a huge mistake in doing so. Also, the fact that you hold two Qs makes it less likely that your opponents will be holding gutshots.

The only way you can protect your hand with a flop check/raise is if LP bets, or if MP bets & LP folds & EP has a hand he'd call one bet with but not two.

All this adds up to a very long way of saying that it is better to just bet the flop.