Faye going back to Georgia for awhile would only make sense for story purposes if she discovered something more about her father's suicide. Quite honestly, if Jeph wanted to do this, he could just as easily have Faye's mother come up to visit her.
I will say we should remember the argument with Faye and Dora was titled The Great Schism. There will be no reconciling between the two right away, for one reason or another. Dora might feel guilty about how she left things, but my guess is she'll feel too awkward about the whole thing to want to confront the issue again - since burning bridges is much easier. And Faye will remain pissed - not so much because of getting fired (either she'll recover, and find a new job, or not, and find different reasons to be miserable) but because when it came down to it, Dora just didn't care about her as a friend as much as she thought.