I'd push here.. Hands that beat you are 88, 99 (why would he bet 4$ if he hit his set?), Q9, 44, QQ.

You are ahead of so many other hands that he could possibly have. I find that the min bet often represents a flush draw. I push here every time. He's much more likely to have KQ, AQ, QJ, QT.. JT or TT and a split is also a possibility.