If I set up an individual account for my daughter can she charge my credit card with an app purchase?
Is Apple ok with it? - yes
Would I do it? - probably not
If my daughter was young, I'd gift her an allowance and augment with larger gifted apps when needed or have some gift cards handy (you can often get them at 20% off at warehouse stores and online from time to time). If she were older, I'd want to get her a credit card account either on her own or tied to mine so she can start on managing her finances.
If neither of the above options makes sense for you, you most likely you will be able to specify your billing address on her Apple ID. Should you be comfortable giving her control over your credit card to make purchases, it's your decision which accounts you choose to store that billing information and who has access to the password and security questions.
I would say that if you want to use that credit card with other Apple accounts, you might find one or both locked so it might be easier to set up an allowance or get her her own credit card (in your name or hers) number so that she has a cleaner setup.
Apple does use the name on the billing contact for the default name on Game Center and some other places, so your daughter might be not only spending your money, but representing you in some of her online activities.