This is a very tough spot. First of all I don't mind betting at a flop like this especially against someone who is being annoying and floaty. I've found that when you bet at flops where its likely you both missed and you both know its likely you both missed you can often level them into not playing back and take it down there.

I think that if I had KQ here on the turn I would pretty much always shove because his line screams of a combo draw. I know that I often prefer to take off a card with a hand like 56, Axcc, A6, etc in BoB and then raise on a whiffed turn. By doing this I can generate increased FE,force you to commit to continue, etc, etc. while also being able to extract a lot of value when i hit.

The only problem is youre holding the worst possible queen and b/c he is such a floater it would not surprise me in the least to see him show up with JQ TQ here (probably with the Qc) and be willing to play for stacks (i know i surely would).

I think that with the read on him (lets remember he could still have air here) and that you are anticipating getting it in light, this is a great spot to charge his draws and shove, hoping not to get shown a better Q.