I think a minimum raise is in order here. The next minimum raise is already sizeable in itself, and screams "get out of this pot. I'm taking it down." But BECAUSE it screams that, it may make a hand like QQ or AKs call, thinking that they have you dominated. KK's probably coming along for the ride no matter what happens.

But I don't necessarily hate your play here either. I think the only mistake here (other than folding, obviously) would be to just flat call the raise. You're opening up an entire can of crap if you do that.