Lucky or unlucky for her, Buffy had been put through rigorous lessons about all sorts of religious and mystical stories that would have any pertinence to her role as Slayer. She didn't want to assume that she was escorting a tiny demonspawn about town, so she tried not to let her overly paranoid, Slayer instincts convince her that Edith was actually Lucifer's child.
"We'll go into one of the stores and see if they can look him up, okay? Maybe someone around here'll know how to call him," she continued. The sooner she got Edith home, the better. Well, maybe not. If her father was some sort of demon worshiper looking to sacrifice the child, she'd have to involved, and then Ambrose would come close to strangling her.