I would say maybe look into getting another ps4 or a gaming desktop. Trying to get another laptop that will run ffxiv will prob cost you close to $1000. If you buy a $400-500 laptop it will perform very similar to the one you have now, pretty poorly.
If your dead set on a gaming laptop. A company called MSI makes pretty decent ones at somewhat good value. You gonna want the G series, thats the gaming one.
This is probably the cheapest you would want to go for ffxiv.
http://www.amazon.com/MSI-GE60-APACH...rds=msi+laptop