Probably not the best setup for XIV... entry level to mid-range laptop config. That AMD 6520M fairs just a little better than Intel HD4000 graphics ( http://www.notebookcheck.net/AMD-Rad...G.55734.0.html )--a large factor may be the shared memory. May not help much either that you only have 4GB of physical memory--a slice of that is getting taken for the video card. It might have done a lot better if they could have integrated memory for that chip. Putting larger (and possibly faster) chips in there may help a little, but mileage may vary with that. Personally, I prefer to start with at least 6GB on anything past Vista.
Look at the details of your Windows Experience Index (right-click your Computer icon and select properties, then click the "Windows Experience Index" hyperlink next to your score). When shopping for a laptop to game on (or desktops too for that matter) , this is a quick and easy way to compare them in the store. Breaking out the Windows Experience Index scores can give a glance at what you may expect out of it. I would hazard a guess your Gaming graphics is falling just under a 6 rating. Ideally, you want this to be at least above 6, preferably close to a 7 or higher if possible to have some of the eye candy on.
Basically, you will need to do some heavy trimming on your graphics settings. Make sure everything in the GPU's own graphics settings (systray icon, or right-click a blank spot on the desktop) are set to either a performance or application control setting. Then, go into the FFXIV graphics settings and start with the base profile for standard laptop settings. Disable all shadows--you, others, etc. I think the Physics settings are already trimmed down, but verify they are set lower for everyone else besides yourself. Turn off cascading shadows and glare points--dropping the quality of detail on shadows to 512 may help a little too, but it can have a very distracting shimmering effect so you may want to leave it at 1024. This should turn off the bulk of the eye candy so your card isn't straining as much. Some other things you can try toggling are the grass settings and such as well, but they may only help in certain zones, and very minimally at that. Toggling the LOD stream option may help a little too, considering the memory constraints you may be facing with that setup.
Probably your biggest bump may come from your resolution settings though. Windowed vs full screen, and how high you put it. Might find yourself rolling back to around 720p (or lower) settings in full screen to get it to a smoother framerate.