I'll disagree with griffey on hand one. I think AQ is pretty likely to fold the flop to a raise so you're just redlining the pot when you raise there. There aren't a lot of live-equity hands against us in his range so I don't think its a particularly profitable redline either, with 8% equity when called.
Depending how much you know about him, the turn could be just a fold. But i def prefer shoving here to raising the flop, or 4-betting pre for that matter.
What was his 3-bet % vs a HJ open?