PS $4 180 MTT: JJ on Q-high flop. Can I let it go?

[Maple Leafs]

I have very little experience at MTTs, even less at final tables. Is there any way a better player avoids going broke here?

PokerStars No-Limit Hold'em Tourney, Big Blind is t2000 (3 handed) internettexasholdem.com

BB (t62927)
Hero (t40060)
SB (t167013)

Preflop: Hero is Button with J[img]/images/graemlins/heart.gif[/img], J[img]/images/graemlins/spade.gif[/img].
<font color="#CC3333">Hero raises to t6000</font>, SB calls t5000, <font color="#666666">1 fold</font>.

Flop: (t11200) 7[img]/images/graemlins/heart.gif[/img], 3[img]/images/graemlins/diamond.gif[/img], Q[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks, <font color="#CC3333">Hero bets t8000</font>, <font color="#CC3333">SB raises to t22000</font>, <font color="#CC3333">Hero raises to t33960</font>, SB calls t11960.

Turn: (t79120) T[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>

River: (t79120) 5[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>

Final Pot: t79120

Results in white below: <font color="#FFFFFF">
Hero has Jh Js (one pair, jacks).
SB has Ks Qh (one pair, queens).
Outcome: SB wins t79120. </font>

3xBB has been my standard pf re-raise all the way through. SB is VP$IP = 21.6%, PF raise = 14.2% and 3.6 total AF (7.0 on flop). I feel like he's certainly good enough to make a play here without the queen from time to time.

Standard line? Am I just stinging from coming so far and then pushing with the worst of it, or was there a better play in there somewhere?

[Maple Leafs]

So... no?