Will I get in trouble for a PCS to Korea with only 6 months left on my contract?

Here are your options:
1) Extend contract to meet obligation
2) Reenlist to meet obligation
3) Sign a Dec Statement.

You will not be going until you are able to meet the 12 months required for the assignment. Either way, you need to seek out your Retention NCO to see what advice and guidance they have. If you do not plan on reenlisting, then Option 3 is the route you will need to go. Which circles around back to you needing to see the Retention NCO.

You can't get in trouble because you can't PCS without reenlisting. Your reassignment section will not cut your orders until you do

Why would you get in trouble? You are on orders to go. This kind of thing happens all the time. SM's PCS to a duty station and have less time remaining in service than is required. Once there a retention NCO will advise you of the possibility of your re-upping and failure to re-upp will mean you exit the service on your ETS date. Not a big thing. I had 4 months left on my contract when I got orders for Korea. I went and up until the last I was set that I was going to ETS and then I changed my mind.