Wow...delicate subject, I would think. It's your friend...do you know of any outstanding circumstance for the nonpayment? i.e. out of work...husband out of work?
A promise is a promise and your daughter deserves to get paid for her time. This is a great opportunity for your daughter to learn assertiveness. I have a few questions:
1. Has she approached the woman herself and asked her for her pay?
2. If she has, what was the woman's excuse for not paying her on the spot?
3. If she has not...why not?
Perhaps the woman has forgotten...we all get busy, or she 'thinks' she has paid your daughter already. Maybe she needs a gentle reminder.
If it were me, I would encourage my daughter to go there (if walking distance), and politely assert herself. I would suggest role playing that scene with her prior to it if she is shy or timid. "Mrs. M, do you remember when I babysat on Oct 6? Well, you asked me to wait for my pay, but its been two weeks and I need the money. I'm just wondering if maybe it slipped your mind?" Remind her that she worked hard for that money and her time is valuable and she deserves this money. I've done role playing with my very shy nephew for job interviews and he thinks it's silly at first, however, he admits it does help.
Then, if that fails, I would take the next step and support her by going with her to your friends house and approach her together. If the woman does not pay up I would find out what the problem was and go from there. Good luck.