Since none of the experienced C1Pro users here have responded, I will give it a shot.....
The quickest way I have found to do what you want if using referenced image files in the catalog, is to duplicate the catalog by copying the entire folder from where it resides to a new location, renaming the database file and the folder name to match (everything else in the folder(s) can remain the same), then remove the stuff you don't want from the new catalog.
I suppose you would do the same if the images are stored in the catalog itself rather than being referenced from their original location, but I never work that way so I don't know if that is the case.