I use Time Machine to backup the drive where my libraries are held and it works fine. Just be sure to occasionally restore a copy (keep both) and open it to verify that it works as expected. You can then delete the restored version and continue with the working library. I'd do that no matter what you use to backup your library.
Are you running a "managed' or "referenced" iPhoto Library?
If it's a "managed" then all you need to do is follow Terence's direction in copying the library to the EHD and opening it to verify it works as expected and has all of your photos before deleting the librrary from your Pictures folder on your boot drive.