PARENTS, listen up (and yes, I know this is NOT the popular answer) --
You can store your credit card info to use with your iTunes account, but as a parent you should NEVER give your underage child YOUR PASSWORD to that iTunes account. When YOU share your password, YOU are opening the account up for that child's use and it is YOUR RESPONSIBILITY to control its use, not the responsibility of the credit card company and certainly not iTunes' responsibility.
Change the iTunes password. Do not give your child any of your passwords for any reason.
We as PARENTS must set the example of RESPONSIBILITY, not blaming others for our poor decisions leading up to bad consequences. Children do not have good judgment in financial matters, that's why they are not allowed to sign contracts. Did the daughter make poor financial decisions? Absolutely. But that is why we have to teach them about finances before we give them access to finances. This girl obviously can do math and knew she was spending funds, but unless she stole your password to get into the account or breached an agreement with you to never purchase anything in iTunes...she actually had permission to do what she did.