Yes, she needs her own Apple ID. Sharing your Apple ID is what is causing this. You should erase the old phone, start over again, get her her own ID and set up Family Sharing if you want to share purchases.
How to erase the phone and prepare it for her to start over.
What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support
Create an Apple ID
How to create a new Apple ID - Apple Support
If your daughter is under 13 and you want of set up Family sharing, see the section in here about setting up an ID for a child.
Family Sharing and Apple ID for your child - Apple Support
Setting up Family Sharing
Set up Family Sharing - Apple Support