So, to give you an idea what you might expect, I've dug up my old manual from 2005, when I bought the game. Throughout vanilla they did update the minimun requirements so I am not sure wether I have the newest. Information on other sites vary alot, but here they are from a reliable source:
-------------------------------------------------------------------------------------------------------------------------------------------
System Requirements
OS: Windows 2000/XP
Processor: Intel Pentium III 800 MHz or AMD Athlon 800Mhz
Memory: 512 MB RAM
Video
Minimum: 32 MB 3D graphics card with Hardware Transform and Lighting, such as an NVIDIA GeForce 2 class card or above.
Recommended: 64 MB 3D graphics card with Hardware Transform and Lighting, such as an NVIDIA GeForce FX 5700 class card or above. For a complete list of supported 3D cards, please visit:
http://www.wow-europe.comSound: DirectX-compatible sound card.
Install size: 6.0 GB.
-------------------------------------------------------------------------------------------------------------------------------------------
All in all: You will probably not have any issues what so ever to play the game on the laptop. Pobably on very high/highest settings. Have fun playing!