Playing The Turn

This is from a $10 MTT on Stars. No read on villain, though as it's the first hour play is pretty loose and a call preflop doesn't tell us much.

Blinds: t50/t100

UTG folds, villain (with a stack of t3015) calls from UTG+1.
All fold to me (with a stack of t2585 - about average) on the button, I call with Q [img]/images/graemlins/club.gif[/img]K [img]/images/graemlins/heart.gif[/img].
SB folds, BB checks. 3 players, pot is t350.

Flop: 9 [img]/images/graemlins/heart.gif[/img] 8 [img]/images/graemlins/diamond.gif[/img] K [img]/images/graemlins/diamond.gif[/img]

BB and villain check. I bet 300, BB folds, villain calls. Pot is now t950.

Turn: Q [img]/images/graemlins/spade.gif[/img]

Villain checks... so now we need to make a decision. This is a situation I often seem to read/play wrongly and would welcome some advice.

Any range for the villain based on that flop call?
Should we bet now with top 2 pair and, if so, how much? A half-pot bet might seem best, but then would we be prepared to fold to a raise (assuming set/straight)? Is a check completely out of the question?

Or is this perhaps simply a hand we might go broke on? Needless to say, I went broke here!

I'd be grateful for anybody's thoughts on this, I'll post the actual outcome later.

Thanks.