Folded KQs 3-handed (originally posted in HU forum)

[beekeeper]

I originally, mistakenly posted this in another forum.

Three players left from a 20 person home tournament which pays 3 places (3rd place gets their buy-in back).

Blinds: $800/$1600.

Me: BB, short stack, with $1200 left after posting.
SB (tight player) has about $1800 after posting.
Button (loose player) has $4000.

The button raises $1600, and the small blind, who has played very few hands and has always had a hand when he makes a move, goes all in.

I have KdQd and fold. Button calls.

I figured I'd be up against an Ace and a medium pocket pair. Bad move?