Hi, dkinhilo,
iMovie for Mac projects cannot be transferred independently. They must reside in an iMovie library, and then you can transfer the library that contains the project to an external thumb drive, or other external drive, that is formatted Mac OS Extended (Journaled). So, create a new iMovie library on your MacBook Air and copy your project over to it. Then transfer the library to a thumb drive and plug the thumb drive into your iMac, where you can then access and edit the project. Both computers must be running the exact same version of iMovie for this to work.
Before transferring the project to the thumb drive, go to the project browser screen (where your projects are displayed as icons) and select the project and do a File/Consolidate Project Media.
Note: Reformatting a drive erases all data that is on it. So if you need to reformat your thumb drive to Mac OS Extended (Journaled) be sure first to back up or remove any data on the drive that you want to keep.
Here's a help link that explains how to work with multiple libraries and transfer projects.
https://help.apple.com/imovie/mac/10.1/#/mov3fa25bae7
-- Rich