If you use "Share > Export > Media Browser" the exported file will be located in the project's package contents folder. When exporting using "Share > Export > Movie" or "Share > Export using QuickTime" (as you appear to have done), you can choose your own location, such as Desktop. Have you checked in your Documents folder and Movies folder? - these are usually the default locations when exporting using the latter two methods.
To access package contents, in Finder go to your Home folder "<your user name>/Movies/iMovie Projects" and locate your project. Right-click (or Control-click) on the project name. From the pop-up menu select "Show Package Contents". In that folder you will see a folder named Movies (provided you have shared to Media Browser). Exported movies will be in the Movies folder within Package Contents. Exported movies will be named Large.m4v, 720p.mov or 1080p.mov and similar (depending on which size you exported as). These can be copied and pasted and then renamed if desired.
Note that projects stored on an external drive will be at the top level in the folder Movies/iMovie projects. Again, any movie shared to the Media Browser will be stored in the package contents folder for the relevant project, as described above.
Having said all this, it's unlikely that you will find your exported movie in the project's package contents folder, given that you exported as "Share > Export > Movie" and "Share > Export using QuickTime". As I described above, when sharing using these methods, you have a choice of locations (unless you've left the setting as the default location, which is possibly your Home folder "Documents" or "Movies".
John