KK on the first orbit

[JDO]

This hand has raised questions in my mind for a while. I think I did ok, but I was curious what the folks on this board thought.

First orbit of a UB 5 or 10 dollar SnG we all have roughly 1000t. I'm on the button with KK. Folded to MP who min raises to 40, one caller between us. I bet the pot (110). Folded back around to MP who calls, the other guy calls as well.
Flop:

QhJd8h

MP goes all-in. I have no reads on him at all. Folded to me. I think for a second and fold.
My reasoning was. Allot of players will make a pot building min raise with JJ-AA, and if that's the case, he's got me beat. Second, it's not out of the question that he has two pair, in which case I am beat. Third, it was to close of a call with not a good enough hand to play. I'm just curious what you all think of my lay-down. I think that my pre-flop raise should have been 50-100% bigger considering how early it was.

After playing the whole SnG with the guy I learned that he could have had any two cards, but that's hindsite...