As one of my common answers to this type of questions, lets check the minimum requirements for WoW:
- Intel Pentium 4 1.3 GHz or AMD Athlon XP 1500+
- 512 MB or more of RAM (Vista requires 1 GB or more of RAM)
- 3D graphics processor with Hardware Transform and Lighting with 32 MB VRAM, such as an ATI Radeon 7200 or NVIDIA GeForce 2 class card or better
- DirectX® 9.0c (included) and latest video drivers
- DirectX-compatible sound card or motherboard sound capability
- 15.0 GB available HD space
- 4 x CD-ROM drive
- DVD-ROM drive for DVD version (Downloadable Installer also available)
- Broadband Internet connection
- For voice chat, an SSE enabled CPU is required.
As you can see, you are way too high from this requirements, so you'll not have any problem running the game maxed out at 1080p mode. WoW it's a good game, but it's not the top graphics game of its family, so, latest computers can run this game very easy because graphics are not something amazing, compared to other games.
Don't be afraid and go ahead and install the game, you'll enjoy playing the game perfectly fine in that PC that you have.
I have a dedicated WoW box based on Phenom II X2 550 and a Sapphire 5770. Runs maxed out on my 50" TV at 1080, on average 40-60fps (unless you go to crazy places like Dalaran, but that's just WoW for you).