Desert planets do not require any special research to colonize. A colony capitalship or frigate should be able to colonize it, provided it has antimatter. The only other things that may stop you from colonizing a neutral planet is enemy culture, shown by the enemy's team color on the phase lane lines, or certain abilities like the Novalith cannon can prevent planets from being colonized for a while. There will be red text on the planet that says "Cannot be Colonized" or something like that if this is the case.

That said, if you have the forbidden worlds DLC, there are Barren and Ferrous planets that look kind of like deserts, but have their own techs you need to research.