Can I get a divorce while I’m in Korea?

Let me take a different approach. You and your husband are in a difficult situation. You are stationed overseas, remote and that puts a lot of stress on any marriage. Additionally, your husband is planning another stressful life event, leaving the Service. The facts that you are young and haven't been married long means you have limited life experience from which to judge your situation. SGT Robert Pryor is correct about the divorce and cost. I recommend you consider counseling now and when you return to CONUS. Start by talking to the Chaplain. Even if religion isn't part of your life style now, Chaplains are good listeners and will have some suggestions for you with regard to your marriage. Don't do anything about a divorce until you return CONUS.

Once you get back to your husband, consider marriage counseling before you decide on divorce. Things will look different when you two can communicate face-to-face. A good counselor may be able to help you both to save the relationship. It worked for my wife and me. We've been married 54 years now.

Yes, you can file from Korea. But he can drag it out under Washington State law anyway, and it will cost you a whole lot more than if you can mutually agree to terms, avoiding lawyers and court time.

... Uh... Basically Put YES"...'
Contact You Base Legal Office,
They Can Get You Started & Let You Know What Needs To Be Done From There..
And I'd Wager "It's Easier Than You Can Imagine & A Rather Common Action".
And You Do NOT Need Your Husband's Consent. ~~ He'll Know When He Gets Served With The Papers.