your problem is that you groaned and tipped off the strength of your hand

Inwardly, not audibly. The audible groan came when the raiser called my push (I should have apologised as the button had yet to act).
The big mistake is number 2, that's an auto push.
Yep, but at this point I was thinking why the f**k did I limp. If AQ is good enough to push with why limp in the first place ? The limp re-raise all in from early position has the benefit of looking like a disguised monster. Calling a quarter of my stack out of position with AQ was not a good move. It should have been an all in or fold. I took the passive route and got punished for it. On balance I should have folded (AQ sucks) and if it was just me and the raiser I probably would. With 8k left and the blinds at 300/600 there was time to pick a better spot.
Nobody is perfect... But one thing you should remember is that a lot of people go broke in MTT because they can't lay down top pairs and overcards.
Problem is with just 20 BB's and the blinds up in 3 mins, if you are going to play you end up comitting a good portion of your stack. If I had raised with my AQ and the raiser called (if he pushed I would have folded) what do I do if there is an ace on the flop (assuming the flop did not have 3 of the same suit) ? I would probably have gone broke regardless, as any bet of the flop (say 3k into a 5k pot) would only leave me with 3k back and basically pot comitted.
I like the UTG limp, for me the big mistake is the call after someone raises to 2k and the button calls, auto fold for me, even if you hit you don't know where you are. I can find a better spot.
Realistically at that point, you are only in front of AJ
On balance RED-DOG's advice probably suits my style of play best. I limped because I didn't want to play a big pot with AQ and wanted to allow myself room to get out if I encountered trouble. The limp/all-in reraise is a move I might make with AK but not AQ (even if it may be the correct play in this case).
This board has been a lot of help to me in trying to improve my game as there are many very sharp players contributing. Unfortunately for me I only seem to analyse my hands AFTER they have been played. All this good advice means nothing if you can't apply it and learn from your mistakes and do your thinking where it matters. Apologies if this post has come across as self indulgent navel gazing but I was so pissed off I just wanted to vent a little.
Have a good New Year.