Q: 2 phones: moving from shared Apple Id to separate family linked ids

your daughter need to create a new Apple ID or you need to create one for her if she is under 13 years old.

A new ID means new account and she will not have access to her old messages because it is linked to your account, you can transfer contacts via Air Drop How to use AirDrop with your iPhone, iPad, or iPod touch - Apple Support

or manually via iCloud and card Contacts: Export and import your contacts and What types of content can I share with Family Sharing? - Apple Support

All good information from TOBALL.

However, her SMS messages are not tied to her Apple ID; they are tied to her mobile number, so they will not be affected by changing her Apple ID.

I think this is true for iMessages sent to her mobile number also, but I'm less sure there.