Playing 3BP OOP

I dont really play MTT's but won a seat into a $600 MTT whilst in vegas

300/500/500
Co opens 1300 (35000)
Hero BB KQhh 5000 covers

Flop QdJd3s (10800)
Hero 5000
Co calls

Turn 6h (20800)
Hero 15k??

Im not a MTT expert is this a spot we would just need to stack off?

Should we be sizing smaller on the flop / turn?

Im assuming the 3B pre is fine with KQs

I was slightly worried my turn bet will just fold out worse as he can still have AQ, KQ, JQ, JJ, QQ, 33