That scene really bugs me. He's clearly got PTS and shouldn't be on the frontline but she's convinces him to change his mind and stay.
That's close to the origin but she was created for a one off gag where the other that the henchmen found her funnier than The Joker rather than an intentional female Joker. Paul Dini and the other writers really liked her so they kept using her until she become a more fleshed out character. Both in the comics and cartoon she has spent a lot of time trying to break away from The Joker, it's the constant fan shipping that seems to make people think they are always a couple/sidekick.
I was curious if you were referring to the new 52 origin from Death of The Family so that she was just a long line of attempts of Joker making a Harley Quinn and she was the only one that survived.