Dark Age of Camelot will run on a system with a dual core processor; however, the game will not take advantage of the dual cores.
If you are using an AMD dual core processor, please make sure you have the updated AMD CPU driver which will resolve some performance issues. AMD's updates can be found at: 
From this page, you would want to select the Utilities and Updates link that corresponds to your processor, and then select the "Dual Core Optimizer" from the list of available updates. Save the file to your computer somewhere you will remember (we'll need it later), and then scroll down to the bottom of the page and download the "AMD Athlon 64 X2 Dual Core Processor Driver for Windows XP and Windows Server 2003." Save this as well and once it is finished, run it and let the installer update your CPU driver. After the new CPU driver is installed (it may ask you to reboot, please do) go back to where you saved the Dual Core Optimizer and run that.
If you are using an Intel dual core CPU and Windows XP with Service Pack 2 as your operating system, you can download a hotfix addressing performance issues with dual core processors from the following page:  You will find the download under the "Resolution" section of Microsoft's KB article.