Hey there buhgmama,
Whenever you set up an Apple Watch for a family member, you have to have Family Sharing set up with that person on your account. You are likely the organizer of the account and will need to enable "Ask to Buy" for your daughter to make purchases. With Family Sharing, there is only one payment method for the entire account; however, if your daughter has a credit/balance on their account, that balance will be used first for purchases.
If you prefer adding money to their Apple ID, this link will help: Add money to your Apple ID balance
To turn on Ask to Buy and allow your daughter to make purchases, please look over the steps for your device here:
Approve what kids buy with Ask to Buy
We think you'll find the information below regarding Family Sharing helpful:
One adult in the family — the family organizer — can set up Family Sharing for the group from their iPhone, iPad, iPod touch, or Mac. If purchase sharing is turned on, the family organizer pays for family members' purchases and must have a valid payment method on file. Check which payment methods are available in your country or region.
You can learn more here: Set up Family Sharing
Take care!