Pub Poker Double Points

Today they had poker at a new place so it was double points. I figured I should show up since I'm trying to make the top 32 this month for their big tourney. I did so badly in the 1st session that I decided to come back for the 2nd. There were only 35 entrants and points were paid to the top 16. I found myself in an interesting hand with 11 left.

Blinds were 1000/500 and I had 1000 left. UTG goes all in for 3500. Next person goes all in for 1500. Next person goes all in for 2000. Big stack calls 3500. I look down at QQ on the small blind. Should I push or should I fold? Seems like crazy talk to even consider folding but double points and I was looking at being in 7th with 7 left if I fold and the big chip stack takes out 3 people. BTW the Big blind had a biggish stack and he was still left to act.

I go all in for my last 1000. BB calls the 3500.

Flop Q and 2 hearts. Big blind goes all in and my heart sinks. I think he's on a flush draw and I'm right. AK hearts and when the turn hits the heart and the river nothing I'm out in 11th instead of at least 7th and my set is no good. Oops.