Apple Music Subscription

No. You can listen to Apple Music and download Apple Music without paying for individual songs. However, if you do want to buy a song that is also still possible. Rights to Apple Music end if you don't have an active subscription but the rights to purchased music do not expire. See the following for instructions on Apple Music and also for instructions for purchasing music from the iTunes Store:

Add and download music from Apple Music - Apple Support

and

Buy music from the iTunes Store - Apple Support

As I said, even if you have an Apple Music subscription you can still pay to download songs from iTunes. To download music from Apple Music without an additional charge, click on the following and read the instructions: Add and download music from Apple Music - Apple Support

Note that on an iPhone you will use the Music app, not the iTunes Store app.

Also note that if your daughter is using her own iPhone you will need to have an Apple Music Family subscription for both of your to use Apple Music. See: Get an Apple Music family subscription - Apple Support and Change your subscription plan - Apple Support