Hi,
There is absolutely no problem with moving an iMovie library to an external drive. The external drive must be formatted Mac OS Extended (Journaled) in order for the library to work properly. Just select the library in your Movies folder on your Mac (Go/Home/Movies) and Edit/Copy, Edit/Paste, it to the external drive. Or, you can copy the library to an external drive by holding down the Option key while dragging the library icon to the external drive. Once you have confirmed that the library on the external drive is working properly, you can then delete the original library from your internal drive, if you want. Be aware that if you need to reformat your external drive to Mac OS Extended (Journaled) you must first backup any data that you want to keep, because reformatting erases all data on a drive.
The reason that you initially want to copy, rather than move, the library is to avoid any mishap in the moving process that might damage the library. So you copy, not move, it to the external drive and then you can go back and delete the original library once you have determined that the copied version works properly.
For safety, you should make a second copy of the library onto a second external drive so that you have a backup to your library.
-- Rich