WoW minimum requirements as of MoP patch is now Pentium D and 1GB Ram if XP and 2GB Ram if Windows 7
You have plenty of power to run it with that system. A video card upgrade would show best performance, while CPU and RAM upgrade are not critical.
I have been able to run it still with a Core 2 Duo 1.8Ghz and a GeForce 7300 Mobile in an old laptop with 1.5GB RAM and Windows XP Pro. My 2nd gaming system is a Core 2 Duo 2.4Ghz which is older than your CPU and I am running on 2GB Ram with Windows 7 32-bit and GeForce 8400GS video card with 256MB VRAM and it runs it with no issues. No lag etc on "good" graphics setting. My main system is a Athlon II x4 620 2.6Ghz with a ATI 5450HD 512MB video card and I can run ultra with 30fps, but I toned it down to high for 50-60fps.
My wife is running Pentium E5400 2.7Ghz CPU and 4GB Ram and 64-bit Windows 7 Home premium with GeForce 9800GT w/1GB VRAM and on ultra settings with 40 fps on 1024x768 resolution. Her build is closest to yours. Try just a newer more powerful video card first. You might be able to save your money vs unnecessary upgrade to CPU & RAM
