Was I Ill Fated or Could I Have Handled This Better?

[Mayhap]

I was in a MTT yesterday. First hand I'm UTG + 2. Everybody has 800. UTG opens for 385. UTG + 1 calls. I have KK. I call. Everyone else folds.

Flop comes brick brick Queen. UTG pushes, UTG + 1 calls. I call. Turn is King. River is a Jack. UTG has QQ, UTG +1 has Ace Ten. Maybe I should have pushed right off the bat? I can't believe the lucky turkey went all in with Ace Ten.

Any tournament wisdom would be appreciated.
Thanks ...