QQ Out of Position

[Newbie236]

UB Nightly $129 20k Bounty

Villain has just joined the table and I have no PokerTracker data on him/her. Blinds are 30/60.

UTG+1 (t1730)
Hero (t2770)
MP1 (t6640)
MP2 (t725)
MP3 (t5050)
CO (t3915)
Button (t7220)
SB (t2475)
BB (t3120)
UTG (t2025)

Preflop: Hero is UTG+2 with Q, Q.
1 fold</font>, Hero raises to t120</font>, 2 folds</font>, MP3 raises to t420</font>, 4 folds</font>, Hero calls t300.

Flop: (t900) 6, 5, J (2 players)</font>
Hero checks, MP3 bets t500</font>, Hero calls t500.

Turn: (t1900) A (2 players)</font>
Hero checks, MP3 bets t1900</font>...

I'm sure I played this crappy. What is the standard line in this spot? With 45BB to start the hand, I'm not crazy about pushing pf. My initial plan was to cr the flop all-in if an A or K didn't hit. Not sure what brain cramp kept me from following through. After the A hit the turn, I don't think I can beat anything. Can you get any chips out of AK in this spot after his/her cb? Should you shove and end it on the flop? I don't like any of my options here. I guess that's why being out of position blows. Do you cr the flop and if you're unlucky enough to run into AA or KK, just shrug it off and move on to the next tourney? Not deep enough pf for set value. Fold pf? Man I stink.