With Windows 7, it is possible to have two full screen copies of WoW open.

Firstly, make sure that your monitors are set up side by side in Windows, so you can drag a window from one side of the screen to the next. This should be easy. Next, start up both copies of WoW, go to Video options, and change the Resolution to "Windowed Mode" and check "Maximized". Both copies of WoW will be on the same screen. Using the Windows key shortcut, WinKey+RightArrow, it will move the active window to the monitor to the right.

Or, set up Maximizer in Keyclone if you're not using Win7. But there's no getting around the performance hit of running two copies of WoW at once; the performance boost you get from full screen mode will be gone if you're multitasking. Sorry.