Although the director confessed "that it took me months to realize I really didn’t have a story," Variety reports he had intended to focus on "The Million Dollar Debut of Batgirl!," story from DC Comics' Detective Comics #359 that introduced Barbara Gordon. Written by Gardner Fox and drawn by Carmine Infantino, the tale follows the daughter of Police Commissioner James Gordon who, dressed as a female version of Batman for a masquerade ball, intervenes in the attempted kidnapping of Bruce Wayne by Killer Moth. Although Batman insists the gives up crime-fighting because of her gender, Barbara ignores the Caped Crusader and adopts the identity of Batgirl.
Although there's no indication what aspects of that story Whedon might have included, it's possible he intended for Killer Moth to be the movie's villain.
Following the success of Patty Jenkins' Wonder Woman, the DC cinematic slate has powered forward with a focus on female heroes, and Batgirl would've permitted Whedon, the creator of Buffy the Vampire Slayer, to write another feminist icon.