I need help with a hand I busted out on.

[PukaPlaya]

I didn't save the hand history on this one but it went basically like this:

Blinds 300-600 + Antes
UTG +1 (8500T)with AK raises the minimum
UTG +2 (14000) calls

Folded around to me. I have JJ on the Button and 8k in chips. I contemplate just calling but the SB is the big stack with about 24k and nearly everytime there are 2 or 3 limpers or minimum raisers he likes to come in for about 10x BB pushing everyone out or getting heads up.

I decide to push and hope to either take it down at best or isolate at worst. UTG+1 is the only caller and flips over AKo.

She hits a A on the flop and I don't improve. If she had lost she would have been left with 500 chips.

Is calling correct for her here? Was pushing correct for me? It seems like everytime I have called in similar situations recently with AK I have lost to pairs. I realize the results don't matter but the correct decision does. Either way I honestly wanted to scoop the pot right there.

So what would you have done?

Related comment:
This villain pissed me off by immediately typing "TY" in the chat window after busting me. When I say it was a coin flip and this time you won, she admonishes me saying I got what I deserved for being "greedy". She of course busted out 20 minutes later missing the money as well which made me very happy.

I realize it is silly to get upset when people type something rude in the chat and usually I can ignore it. This time it bugged me and helped prompt me to post.