If QJ is in his range so is KT and T9
and there are plenty of villains that will overplay AK
And you have outs against QJ...
So meh, getting it all in with bottom set here isn't terrible but I don't like it.
When you shove like this, you are pushing out hands you beat. AK folds probably 75% of the time, and KQ folds probably 90% of the time. You probably fold out T9 30% of the time. So all that is left here is TT, KT, and QJ
When we flop monster, its important that we still play in a way in which lesser hands can call. And when you essentially 4-bet jam flop you ensure we are only called by the top of his range. I like the raise (sizing is fine though it could be $40 - $45) but when he 3-bets, I'd flat to keep his range wide as possible.
I'm also a big fan of flatting 3-bets (or raises) on the flop when I'm monster AND IN POSITION. Since we are in position villain will have to continue his aggression on the turn, so this way we keep in more of his air and lesser hands we beat.
In any event, this is probably a cooler type hand and we ran into QJ, but I'd still like to keep in as many AK and KQ hands as possible. Flat the 3-bet and then on turn V will likely shove into you and then you can call. This line would keep in more hands that we beat.