I decided to slowplay these Queens. I don't slowplay often, but during my losing streak I'm trying to avoid big pots with semi-strong hands.

Thoughts.

Party Poker No-Limit Hold'em, $ BB (6 max, 6 handed)

Hero ($70.68)
SB ($52.44)
BB ($30)
UTG ($39.15)
MP ($54.80)
CO ($63.85)

Preflop: Hero is Button with , . SB posts a blind of $0.25.
1 fold, MP raises to $1, CO calls $1, Hero raises to $4, 2 folds, MP calls $3, CO calls $3.

Flop: ($12.75) , , (3 players)
MP checks, CO bets $3, Hero calls $3, MP calls $3.

Turn: ($21.75) (3 players)
MP checks, CO checks, Hero bets $11, MP calls $11, CO folds.

River: ($43.75) (2 players)
MP bets $20, Hero calls $20.

Final Pot: $83.75
Main Pot: $83.75, between Hero and MP. > Pot won by MP ($83.75).

Results in white below:
MP has Td Ad (full house, tens full of sevens).
Hero has Qs Qh (two pair, queens and tens).
Outcome: MP wins $83.75.

Bad luck, what can you say. 5 outs on the turn, he caught one.

I would definitely raise the turn, at least 3x his bet, probably to $10 here. You were the preflop raiser, make a "continuation bet". His $3 bet into $13 pot is like a check. I don't want to let him draw cheaply to an A/K on the turn.

I might check behind on the turn, but I want to raise the flop and control the action. You get better info this way, if you raise the flop and he leads strong on the turn, you know he likes his hand.

Poker2006 is exactly right

You have to raise on the flop. If they both fold thats okay because they didnt have anything. Therefore, you were not going to get any more money out of them unless they caught up..