Party $20+2 NL...what did I do wrong here?

[Go Blue]

So this hand is from the Party $20+2. This is the point where I was eliminated so I'm wondering if I could have done anything different here to either take down the pot or get away from the hand.

This is just after the first break, so around half the field is left and my stack is just below average at around T1800. I am in MP. The person to my right, who has a stack of around T4500 or so min-raises to 200. I have AKs. I don't want to risk losing a lot of chips here yet I know it's a good hand. I decide to min-raise to hopefully get everyone else to fold and to isolate the opponent to my right (who, I should add, has made some raises with a couple of questionable hands). I decide that If I flop the top pair or a flush draw, I will go all in almost no matter what and if I don't, then I will probably not commit too many chips.

Anyway, one other person (also a big stack) called and the raiser called. The flop came KQ4 rainbow. That's something I liked at that point and I figure that the only hand I should be worried about is KQ. So the guy to my right bets for 100 and I move all in as planned. The other big stack folds and the bettor calls with KQ. I'm out.

So, let me have it. What should I have done here? I'm really not happy with the way this turned out. Should I have just pushed preflop or something? Thanks in advance.