I guess there is just nothing that you can do against a player that has a good draw except fold.

PokerStars No-Limit Hold'em, $1.00 BB (9 handed)

MP1 ($113.85)
MP2 ($102.75)
MP3 ($112.25)
CO ($31.50)
Button ($55.10)
SB ($108.10)
BB ($129)
Hero ($86.65)
UTG+1 ($23.40)

Preflop: Hero is UTG with , .
Hero raises to $5, 3 folds, MP3 calls $5, CO calls $5, 3 folds.

Flop: ($16.50) , , (3 players)
Hero bets $13, MP3 folds, CO calls $13.

Turn: ($42.50) (2 players)
Hero bets $18, CO calls $13.50 (All-In).

River: ($74) (2 players, 1 all-in)

Final Pot: $74

Results in white below:
Hero has Ad Qh (one pair, queens).
CO has Tc Jc (straight, queen high).
Outcome: CO wins $69.50. Hero wins $4.50.

First, I hate AQ so I likely just limp preflop. I bet out the flop which would be a much smaller bet since the pot wouldn't have been raised. On the turn, you have to expect that if you are ahead, you likely aren't ahead by much because of how that board is. Co was short stacked which means he probably wasn't getting away from this hand no matter what.