Hm, well.

First of all, you say you are both interested in BDSM, ask her if discipline is a turn on... because it doesn't always act as a punishment, and if she is a good girl, then, why punish her?

Secondly, role play can make everything easier, if she is interested in discipline, as she can act the naughty and rebellious type, and be punished accordingly in the play, but wont feel any sort of resentment or guilt in her real life about being punished for nothing.

This also makes it easier for the sub, especially if you keep the D/s thing solely for play time, as you both do.

Besides, think of the possibilities - she is a naughty school girl, a insolent maid, or perhaps she hasn't been a good girl, and her Daddy needs to teach her a lesson.

Whatever your poison, just talk about it maybe, and make sure she knows that she hasn't done anything wrong. Just to avoid any sort of hard feelings or upset in an otherwise playful D/s relationship.

Thats my advice.