I have not tried this so I'm not sure exactly what file to transfer, but the config files are in Documents > My Games > Final Fantasy XIV - A Realm Reborn. I have 2 folders (assuming 1 for each of the characters I have) and 2 files, one FFXIV.cfg and FFXIV_BOOT.cfg. If I had to guess, it's the folder you want to transfer, it should be named something like FFXIV_CHR002340234023B. As far as I can tell, there's no way to tell which folder is for which character.