Help with my daughters Apple music account

She will need to have funds on her Apple ID account (account balance, like store credit) on the due day. If such funds are not there on the due day, then the subscription will expire.

Alternatively have a automatic valid payment method (e.g. a card) tied to her Apple ID account, to be used instead of (or in addition to) Apple ID account balance.

You can’t specify to only pay for her music: there is no distinction between all kinds of purchases that are charged to her Apple ID account. Many parents that choose to pay for the music subscription of their child, will have to give a sum of money monthly and trust that it will be used for music. If the Apple ID account balance is used for other App Store purchases, then there may not be enough balance left for the subscription.

Another option is the Family Subscription, if there is enough interest in such a service within a family group.

Payment methods that you can use with your Apple ID - Apple Support

How to add funds to your Apple ID - Apple Support

App Store & iTunes Gift Card - Apple (not Apple Store Gift Cards; beware of the distinction). Gift cards can be physical cards, or electronically as a code in an email message. They can be any value between $10 and $200. Note that tax may be added to US subscription prices.

View your Apple ID balance - Apple Support

The Apple Music Student subscription will need monthly payments, on the same day of the month as the subscription was started. For active subscriptions, the next billing date can be found in the subscriptions overview, on her iPhone or on her computer with iTunes.