My daughter was using my Apple ID with her Ipad mini. I want her to use her own Apple ID now that she is old enough. How can we transfer the content of her ipad mini, ( music, photos, apps) particularly game apps WITH THEIR DATA onto her new account? She doesn't want to start from scratch with all her games.
You cannot. It's not possible to share content from one Apple ID to another. Apple actually recommends everyone have their own Apple ID.
You can load the content on your daughter's device and she can access them all normally. You can then log her into her own Apple ID, where she can begin to make her purchases on her own account. The only downside is she will have to know your Apple ID's password as iOS will ask for it on rare occasions (when restoring the device for example). It's possible to store content from multiple Apple accounts on a single device, the user will just need to enter the password should the OS ever require it. That is the only feasible solution in your case (other than starting over). This will at least circumvent having to re-purchase any content.
This has always been a sore spot for Apple customers as they have historically been very firm in never being able to even close an Apple ID, let alone share content between them.
You can read more about Apple IDs here: http://support.apple.com/kb/HT5622?viewlocale=en_US&locale=en_US
With the release of iOS 8, you can.
There is a new feature called family sharing which allows you sync purchases from 1 apple ID to another. You could set up a family with your daughter where she can re-download her games.
If she wants her data (progress ect.) you could use apps like iFunBox to extract the data and transfer it to another iPhone.