Hello,
Congratulations! A  NEET score of 609 you will get you mbbs seat in top medical colleges under both  uttarakhand state quota and 15% all india quota.

With a 609 score your overall percentile will be 99.08 - 99.26 and your NEET AIR Rank will be around 1500 - 1291.

Yes if you do mbbs from medical college of karnataka you are eligible for post graduation from the state too.

However with the current dissolving of mci and changing of neet pg to next exam a lot of changes are said to be brought up in the medical post graduation curriculum.

You can use careers360 college predictor to know the colleges you can get at your NEET score;- https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer