Term originated on Live Journal (adapted to Tumblr) for Robert Downey Jr (RDJ) fans. In a video, RDJ introduced himself as Rubber Ducky Jr, to which LJ user UltraDowney (Jakob-Dylan on Tumblr) developed the nickname for the RDJ fandom.
Guy: Iron Man is an awesome movie
Girl: Yes! Robert Downey Jr is the best actor! I am totally one of the ducklings.
A group of people who follow an authority figure as literal ducklings, baby ducks, follow their mothers in the wild.
House: Could you stop flocking around me like a bunch of ducklings?
Cameron, Chase, and Foreman: No.