I would just push this. Mini-raising practically screams AA/KK.

Also, mini-raising doesn't always maximize your value here. If you mini-raise you give them an opportunity to get away from the hand on a bad flop. For example, QQ or KK on a ace-high flop (and king-high flop for QQ), or a whiffed AK. Those hands likely call your push anyway, and you prefer the money in now with those hands so they can't get away.