Ok I was going to say this card may not play it but after reviewing the stats and comparing them to my stats (GPU only) you should at LEAST be able to play this game on medium settings. I'm using a GT 9600 which is lower then your card and I have no problems running the game on 1920x1080 in the FFXIV Config with no AA, 8 General drawing, 3 background, lowest Shadow, DoF on, Ambient OFF, Texture qual and filtering High. Sometimes in Ul'Dah it can get a little slow on rendering the NPCs or PCs but otherwise, I have no issues.
Edit: Added this for reference
-=-=-=-=-=-=- System Information -=-=-=-=-=-=-
Operating System Microsoft Windows 7 Service Pack 1 64bit (build 7601)
Processor Intel(R) Core(TM) i5 CPU 750 @ 2.67GHz
Number of Processors Logical Core Count 4 Physical Core Count 4
BIOS BIOS Date: 08/21/09 20:06:55 Ver: 08.00.15
Language English (Regional Setting: English)
Physical Memory 12279.055MB
Virtual Memory 2047.875MB
Page File 24556.305MB
Storage C:\ Hard Disk Drive Total Disk Space 297.991GB Free Disk Space 179.732GB
Storage D:\ Hard Disk Drive Total Disk Space 596.170GB Free Disk Space 395.270GB
Storage E:\ Hard Disk Drive Total Disk Space 298.081GB Free Disk Space 93.599GB
DirectX Version DirectX 11
Graphic Device(s) NVIDIA GeForce 9600 GT
+Device \\.\DISPLAY1
+Chip GeForce 9600 GT
+Maker NVIDIA
+Video Memory 487.563 MB
+Shared Video Memory 3583.906 MB
+DAC Type Integrated RAMDAC
+Display Mode 1920 x 1080 (32 bit) (60Hz)
+Driver nvd3dumx.dll,nvwgf2umx.dll,nvwgf2umx.dll,nvd3dum,nvwgf2um,nvwgf2um
+Driver Version 8.17.0012.8026
+Driver Date 8/3/2011 7:50:00 AM
+Driver Language English
+Vertex Shader 3.0
+Pixel Shader 3.0
+Vertex Texture Supported
Graphic Device(s) NVIDIA GeForce 9600 GT
+Device \\.\DISPLAY2
+Chip GeForce 9600 GT
+Maker NVIDIA
+Video Memory 487.563 MB
+Shared Video Memory 3583.906 MB
+DAC Type Integrated RAMDAC
+Display Mode 1440 x 900 (32 bit) (75Hz)
+Driver nvd3dumx.dll,nvwgf2umx.dll,nvwgf2umx.dll,nvd3dum,nvwgf2um,nvwgf2um
+Driver Version 8.17.0012.8026
+Driver Date 8/3/2011 7:50:00 AM
+Driver Language English
+Vertex Shader 3.0
+Pixel Shader 3.0
+Vertex Texture Supported
Sound Device(s) Speakers (High Definition Audio Device)
+Device ID {7DCFCC8E-A4AE-4B6E-8D3C-0A7716F10BB9}
+Device Name HdAudio.sys
+Driver Version 6.01.7601.17514
+Driver Language English
+Driver Date 11/20/2010 6:44:23 AM
Sound Device(s) Digital Audio (S/PDIF) (High Definition Audio Device)
+Device ID {18B91818-714B-4C5E-BA06-C5635323DD3A}
+Device Name HdAudio.sys
+Driver Version 6.01.7601.17514
+Driver Language English
+Driver Date 11/20/2010 6:44:23 AM
Sound Device(s) Digital Audio (HDMI) (High Definition Audio Device)
+Device ID {E96572B7-DB17-44D0-A0E6-134B4DCC2012}
+Device Name HdAudio.sys
+Driver Version 6.01.7601.17514
+Driver Language English
+Driver Date 11/20/2010 6:44:23 AM