$27s - QQ, drawy flop, A on turn

[imsobroke]

PokerStars No-Limit Hold'em Tourney, Big Blind is t20 (9 handed) Hand History converter Courtesy of PokerZion.com

MP1 (t1500)
MP2 (t1440)
MP3 (t1580)
CO (t1410)
Button (t1590)
SB (t1480)
BB (t1500)
UTG (t1500)
Hero (t1500)

Preflop: Hero is UTG+1 with Q[img]/images/graemlins/club.gif[/img], Q[img]/images/graemlins/diamond.gif[/img].
<font color="#666666">1 fold</font>, <font color="#CC3333">Hero raises to t80</font>, <font color="#666666">2 folds</font>, MP3 calls t80, <font color="#666666">1 fold</font>, Button calls t80, SB calls t70, BB calls t60.

Flop: (t400) 9[img]/images/graemlins/club.gif[/img], 5[img]/images/graemlins/heart.gif[/img], 8[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(5 players)</font>
SB checks, BB checks, <font color="#CC3333">Hero bets t300</font>, MP3 folds, Button calls t300, SB folds, BB folds.

Turn: (t1000) A[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, Button checks.

River: (t1000) J[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, Button checks.

Final Pot: t1000

Should I bet anywhere else past flop here? After A hit I was content to shut it down, even if he did have a fd.