I hired an idiot as my replacement

I am a first-time manager, and while I am doing pretty well in most aspects of my new position I made one exceedingly boneheaded decision almost right off the bat: I hired an idiot as my replacement. I really think she has emotional problems. (She recently told me she used to be on psychiatric drugs, as a matter of fact.) This is an extremely high-maintenance employee who cannot seem to make a move without asking for directions. I have learned, thanks to her, that there is indeed such a thing as a stupid question. She wears micro-miniskirts and does not know enough to close her knees when sitting or to bend at the knees instead of at the waist. I could say something about this to her, as it is a violation of the dress code, but our department manager dresses the same way if you can believe it. She has a chronic medical condition, which is not a problem except that she told us during interviews that she had never had a problem managing it at work. Now she tells me that because of her condition she can't work overtime (this is an overtime-intensive industry). I so want to fire her when her 90 days are up, but I feel sorry for her. I also feel guilty that I didn't check her out better. And she is so obnoxious I worry that nobody else will be stupid enough to hire her.