The DesktopServer program is built on XAMPP, so you could export the database and contents and provide that information to your developer. Most developers should be familiar with that process, however the general process is outlined here: Moving_WordPress#Moving_to_a_New_Server
Now, I don't know if you are using the free or commercial version of DesktopServer, but the commercial version also includes an automated "Export & Archive WordPress Websites" feature. Providing your developer also uses the commercial version of DesktopServer, that could be another way to get the information to them.