The items purchased under your "family ID" (or any Apple ID for that matter) cannot be transferred to a different Apple ID. There are several options for sharing purchased content, however, you will also need to authorize the new computer under iTunes with the Family ID. Once you have authorized it for that ID, you can sign it out of iTunes and sign in your daughter's new ID for future purchases:
iTunes for Mac: How to copy purchases between computers
If you want the purchases to be "owned" by your daughter's new Apple ID, you would need to purchase them under that ID.
Cheers,
GB