Did I play my Queens right?

[ShadowSpeak]

Hi guys, I really need some advice on a hand I played at a tournament today. I was wondering if anyone could help me with this. Blinds are 600/1200$

Everybody around the table folds.
Late position calls 1200 minimum bet
SB calls the remaining 600$
I'm looking at QQ in BB. I raise 2000$ from my 9900$ stack.

Flop comes J diamonds, 6 spades, 3 spades.

LP and SB each check.
I go all in with 7900$
LP calls
SB calls
We flip, and LP is holding 6/2 offsuit, semi-bluffing a 6
SB holds QJ spades, giving him a flush draw
Turn comes K spades, giving SB the flush
River 6 clubs, giving LP trips
I end up with the 3rd best hand

Did I play this right by protecting my hand? Flush draw obviously wasn't getting the right pot odds. Then again, I think I could have checked and waited to see if a third spade hit the board and then make a probe bet, folding to any resistance. LP just got lucky so I'm not even worried if I played him right.

Your thoughts?

Thank you.

Shadowspeak*