You'll be fine :-)

My current comp is AMD Phenom II 2.90 Ghz processor 6GB memory, AMD Radeon 6850 graphics card ran Version 1 which was more graphically demanding and runs ARR beautifully with no problem. As you can tell by the processor speed my comp is dated, I updated the graphics card a few years ago, still runs everything I play just fine.
Mostly graphics card, processor speed & memory are the 3 main things to focus on for gaming.

FXIV: ARR Minimum System Requirements

Operating System: Windows® Vista 32/64bit, Windows® 7 32/64 bit
Processor: Intel® Core™2 Duo
Graphics: NVIDIA® Geforce® 8800 Series, ATI Radeon™ HD 4770
Memory: 2GB (4GB recommended for 64bit OS)
Disk Space: 20GB.

You may notice that these are lower than the minimum system requirements for v1.0. This is because Square Enix wants the game to be more accessible and run on a wider range of PCs.

FXIV: ARR Recommended System Requirements

For the best performance you should aim to run the game on a system with at least these specifications.
Operating System: Windows® 7 64 bit
Processor: Intel® Core™ i5
Graphics: NVIDIA® Geforce® GTX 660 or higher, AMD Radeon™ HD 7950 or higher
Memory: 4GB of RAM.
Disk Space: 20GB.