Can I change my assignment to Korea given these circumstances?

Korea is considered a Priority 1 assignment to to the transformation so it’s really going to be hard. Being that your wife’s due month is September and your report is December, that’s enough time to apply for the passport for your newborn. The most, if any they will do is you give a 30-60 day deferment.
You can elect to take an accompanied/command sponsor tour which will allow your family to accompany you to Korea. You and your family will love Korea, I was stationed at Camp Humphreys in September 2012 on a 1yr tour and ended staying there for 3yrs and still didn’t want to leave. Camp Humphreys is a great place to be if you have to go to Korea. I hope this helps...good luck to you and your family...

If you are going to Humphreys, you can go as accompanied or command sponsored. If you do that, it is a 2 year commitment. And you will have to apply for it and do the paper work to ensure that you can drive a POV. If you go unaccompanied, it is a one year commitment and you won't be able to drive a POV. Rules may have changed.

I have yet to meet somebody who doesn't like being stationed in Korea. In the old days, people would rotate in and out of Korea just to be back to Korea. There is a lot to do and see in Korea. They always have something going on around the year.

You can try calling branch. My husband had a similar issue. I was due dec and he was set to PCS this month. It depends on if the assignment is unaccompanied or not. I would just try calling branch and explaining it.