I would flat call here..

AQ off is a marginal hand in this situation. The hands that the villian is gonna call your shove with are pretty powerful against the AQo as he isnt really leaving himself pot-commited with the original raise (although he would be v. shortstacked with the fold) and assuming a good player their only gonna call with a strong hand. At best I think your looking at a coinflip situation here, its quite likely you might be up against AK/AQ or at best AJ/AT but most likely a pocket pair - he was leaving himself v.shortstacked with his raise which would make me put him on a fairly big hand (in a 5-handed game) like a pair.

Also, because your on the button and have position shoving is disadvantaging you by taking away your positional edge. May have been a better play to smooth call and shove the flop if he checks (esp with the benefit of hindsight lol).

Push it all day long. You have big stack and can afford to lose if you are behind.

He can fold so many hands if you push there:

Low pairs which are a minor favourite against you
KT/KJ type hands which can outflop you

How do you react if the flop comes down all low and he shoves? You have to fold possibly the best hand or call with A high. Neither is ideal, let him make the decision.