KK push...am I a donk?

This a a situation that I feel like I made a mistake, but I am unsure of what a better decision would be.
Pacific Poker Satellite to 30K guranteed. Top 39 get a seat in the event, with 1-39 getting the same prize. With 50 players left, I am 14th in chips with 3942. Blinds are 200/400 so I have a little less than ten big blinds.
Big Blind is 12th in chips with around 4000 chips. I am the small blind, and have been playing very tight, and am content to coast into a seat. It is folded to me in the small blind where I have KK. I push, thinking the big blind will not call risking losing and having to put the rest of his stack in on the blind the next hand. Sure enough, I am instacalled by A9, and he catches up and
I have to buy in directly to the event. This may be a really easy fold, but I just thought it was too weak tight to fold KK vs a random hand in the BB. What would be a better line to take in this situation.