Thanks for quoting the 6 months. Let us say that the couple doesn't want to get the divorce RIGHT now due to some situations and they decided to quit Qatar job and return back to the USA. They can initiate the divorce in USA once the residency requirements are met.Georgia isn't an option at this time because one party must be a resident for 6 months before action. So strike that and it is a Non-US law question.
Let's assume the couple decides to drop the divorce matter because it's too costly or the Qatar employed spouse will have to give up his job due to the divorce and they decide to leave it and go to UK to retreat. Where the UK spouse is from. They can very well use the UK to divorce, JUST Like the other spouse can use US to divorce her.
Regardless each country has its own laws to abide by. And am sure when they retain a family law attorney they will work it out what is best for them. Things change. Just because they asked the question today, don't necessarilly means that they will file for divorce tommorrow.