Any basic laptop can run accounting software such as QuickBooks and Peachtree. You will likely also use Excel as well or other similar spreadsheet programs like Open Office (which is free; Google it). A mobile Intel Core i5 is not an absolute necessity, but a powerful CPU can help make the laptop have longer useful life before you feel the need to upgrade to something better.
This $300 15.6" Toshiba Satellite can handle those programs just fine with it's Pentium G2020m CPU (Sandy Bridge generation CPU). The integrated Intel HD graphics core is fine for watching 1080p videos. It's a bit heavy, at 5.6lbs, but it's not as expensive as the Dell XPS 13 Ultrabook...