How to play MTT hand?

[Poker4Living]

$20+2 Deep Stack tourney on PokerStars (5K starting chips, 30 minute levels). 297 players, 76 remaining, 45 placed paid. My M=10.

I pick up AKs in late position. I pop to 3X BB which was my standard at the table. Min reraise by the button. Everyone else folds. I shove over the top. Instacall. He has AA.

I probably could have held on until the money, but just barely, so I figured let's try to get some chips and make a run for real money.

Did I do the right thing?