My daughter and I have been sharing one iCloud account for our iPhone. She has her own Apple ID to purchase music. I need her to have her own iCloud account as mine is running out of storage. She is afraid if I delete her phone from my iCloud in my settings she will lose all of her contacts etc. Then is there a way to move items from one iCloud account to a newly created one?
When your daughter disconnects her phone from the shared iCloud account (by deleting it in Settings) she will be given the option to keep her contacts, calendar entries etc. on the phone. Afterwards just create a new iCloud account directly from the phone.
First to be sure to backup the important contacts, ask your daughter to backup contacts using a Google Account.
Steps are mentioned here
After backing up the contacts just make another iCloud account and use it on one of the phones.