bubble push Q4?

Party 10+1, down to 4 people, Blinds 100/200, chips est. after posting blinds.

UTG - 5400 chips (folds)
Button - 600 chips (folds)
Hero SB dealt Q4 - 1200 chips (push all in)
BB - 500 chips (call)

My thinking is that he will fold and wait for the other short stack to bust-out, unless he has a great hand. He calls with A3 and holds up. Should I have just mucked?

Thanks in advance for all replies.