Will there be a problem with running Comodo Dragon Browser with my McAfee antivirus program on my Windows 8.1 laptop?
No, there won't be a problem installing and running the browser on your computer. This is just a customized browser that works normally. The source is Chromium and it's something more like Chrome, only that's customized with a features missing from the default Chrome application.
Download Comodo Dragon Internet Browser: https://www.comodo.com/home/browsers-toolbars/browser.php