I've heard that personal and business issues don't mix, and in my business its kinda the same. Keep business , business.
I'd try to keep it undercover the best you can at work.
This is unrelated but I'm curious (and somewhat serious) since I've never been in that position. You mentioned being in a position of authority over her, but if you were dating her could you take her over your knee and reprimand her at the office and it would be cool, or could you still get into trouble over it??
I've always just worked at the family business, I have no outside experience and there is no one there I'd be interested in spanking.
Good luck.