I'm honestly surprised WiFi is still as crap as it is. It hasn't been good since day 1 and doesn't seem to have improved much since the early 2000s. I've ended up using powerline adapters and wire connecting all my devices (excusing mobile and tablet). As long as the wiring in your house is good, you'll get significantly better and more reliable speed/connection. You do need to be near a plug socket, but depending on where your girlfriend likes to sit on her laptop, that might not be an issue. Powerline adapters are pretty cheap too.

I highly doubt it's FFXIV for all the reasons people above have mentioned. Outside of trying the above, you could look at upgrading your WiFi box and checking out how old her laptop is and if the issue is her hardware being dated. That would likely end up being pretty expensive however.

Edit: To clarify I'm talking specifically about the powerline adapters that have ethernet slots to wire connect devices