Full Till $400k Guarantee Agony

[RoccoTerrier]

First of all, I have been following this board for a while and it has been incredibly helpful. I am an OK, but not great player who is trying to get better.
Yesterday, I played in an $8 super satellite that got me en entry into the $50/5 satellite which got me an entry into the $400k guarantee. Yay! Three and a half hours into it, there were approximately 375 people left and 351 were getting paid. I was in 255th place and had approximately 12,500 chips. The blinds were 340/170 with a 75 ante. I was dealt QQ UTG and raised to 2200. Everyone folded to the button who reraised to 7800 (he had approximately 18,000 chips). I pushed the rest of my chips into the center. He called and my QQ lost to his AQ when an ace came on the river.

Questions: Regradless of the outcome, was my play smart or stupid? On the one hand, I really wanted to at least make the money (even winning only $200-300 on an $8 investment is nice), but I felt like I really didn't have that many chips and I needed to accumulate to make a play for some great money.

Side question: How do you deal with those crushing bad beats? AQ for crissake.....