Preflop: I would fold. QTs might be arguable and QJs+ is pretty much a clear call.
Flop: I don't like raising with about a 5.5 out draw (4 for gutshot and 1.5ish for bd flush, very rarely are your queens good here, you are usually dominated), but you got a free card so it was okay in this case.
Turn: Definitely bet out when it gets checked to you. Everyone else seems weak, and even if they call, you have at least 8 outs.
River: In a pot this big, I would take a shot, but there is a much better chance of success if you bet the turn.