Transferring iPads

My daughter had (it stopped working) an iPad Air II. I had it set up with my Apple ID so that we could share purchases. However, I didn't connect it to my phone number or email. (I made a gmail account so that she could use FaceTime and Messenger.)

Now that her iPad has died, I wanted to transfer her "set-up" to an old iPad mini of mine.

I erased the mini. Signed back in with my Apple ID, but it won't let me restore any backups that aren't my old mini backups.

How can I transfer her iPad Air II back up to this new mini?