There's another more cleaner way to do this is to go into your FF14 game folder and look for the ffxivconfig.exe, this will open the UI Backup Tool. Click "Backup" and save the generated FFXIVconf.fea file on anywhere in your current PC and copy over that .fea file to the new PC. Next, open ffxivconfig.exe again in your new PC, click "Restore" this time and select the FFXIVconf.fea again. You can ignore the "Do not overwrite older data" checkbox if you do not have any settings made in your new computer.

All your UI/hotbar/gearsets will retain the way you last save them. However, positioning of some UI will be off if your new PC's screen resolution is different.