How to play junk OOP

Battle of the blinds; I'm in BB with AKo. Folds to SB who completes; I raise to $0.30, he calls.

FLOP:
Js Ac 4s

SB bets $0.60
I pop to $1.20
SB calls $0.60 (awesome)

TURN: [Js Ac 4s] Qh
SB bets $1.65
I min-raise (would be all-in for SB to call); SB instacalls.

From this, what do you expect SB to have? QJ? AQ? K10?

Watch and learn, my friend, watch and learn:


Next time there are two overs and a straight draw on the board, I'll try to remember to make a committing bet on the turn so I can hit my 5-outer...