Hi, Jody Joy,
Here's a link to an online help help menu that explains how to copy or move projects from one computer to another.
https://help.apple.com/imovie/mac/10.1/#/mov3fa25bae7
Projects can only be moved from one library to another. Or, you can move the library that contains the project. It's easy to create libraries, so you can create a library to store that one project, and then move the library wherever you want. To move a library to an external drive the drive must be formatted Mac OS Extended (Journaled) to avoid loss of data.
I think that the easiest way is to move your current laptop library from your laptop to an external drive, and plug the external drive into your desktop computer.
Alternatively, you can create a new library on your external drive. Then move or copy the project from your laptop to the library on your eternal drive. Then you can plug your external drive into your desktop computer.
-- Rich