Hi,
Copy-Paste the iMovie library icon to an external drive that is formatted either Mac OS Extended (Journaled) or APFS. . Then plug the external drive into your new Mac and Copy-Paste the library to your new Mac. If you need to reformat the external drive be aware that reformatting erases all data on the drive. So, before reformatting, back up any data that you want to keep.
Before copying the library to the external drive, do an Edit/Consolidate library media to make sure that the library contains all of the media that is used in the projects. That might address the missing links issue that you mentioned. Further regarding the missing links, that could happen because your old iMovie library contains legacy media (outdated formats) that no longer works on the newer version of iMovie. With Mohave 10.1.12 you can do a File/Check Media for Compatibility and if there is legacy media your will be given an opportunity to convert it. This should be done before you copy or transfer the library because the conversion feature is not available after Mojave 10.1.12 so you won't be able to do the conversion in the new iMovie version.
When you double-click on the Library's icon on the new Mac, it will open in the newer version of iMovie that you have on your Mac. Once you open it in the new version your old iMovie version will no longer be able to open the library.
The safe practice is to copy, not move, the library anywhere until you are sure that everything is working exactly to your satisfaction with the library that is copied over. Copying the library will leave you with a backup on your old computer in case anything goes wrong. You will also still be able to open the backup on your old computer with the older version of iMovie that is on it.
I would keep your old iMovie version and its library as a permanent backup. either on your old computer or an external drive.
You might do a little internet reading before doing anything in case I might have missed something. So, as a caveat, whatever you do you will be doing at your own risk. You should be O.K. as long as you use backups, that is always recommended.
-- Rich
