NL10 - JJ - A Preflop Dilemma

[JustARogue]

Poker Stars - No Limit Hold'em Cash Game - $0.05/$0.10 Blinds - 6 Players - (LegoPoker Hand History Converter)

SB: $18.65
BB: $20.20
UTG: $7.20
Hero (MP): $7.95
CO: $10.00
BTN: $17.90

Preflop: Hero is dealt J[img]/images/graemlins/heart.gif[/img] J[img]/images/graemlins/club.gif[/img] (6 Players)
<font color="red">UTG raises to $0.40</font>, Hero calls $0.40, CO calls $0.40, BTN calls $0.40, <font color="red">SB raises to $3.00</font>, 2 folds, <font color="red">Hero raises all-in to $7.95</font>

I'm not fully stacked here because I just lost a hand and didn't hit the reload chips button fast enough.

My thought process on the hand is to call with JJ in position on the raiser and get aggressive on any flop without an ace on it. I don't like to two callers behind me, but figure that the SB re-raise is just trying to pick the juicy pot right then and there. I figure push now and don't get out played on the flop.

I figure I'm only getting called by KK+ and AK+ and ran it through Pokerstove:

equity win tie pots won pots tied
Hand 0: 40.081% 39.87% 00.21% 114702624 596634.00 { JJ }
Hand 1: 59.919% 59.71% 00.21% 171771180 596634.00 { KK+, AKs, AKo }

Does my fold equity make this push ok?