Q: How can I backup an iPod to a iPhone?

What happens when you follow the instructions here: Transfer content from an iPhone, iPad, or iPod touch to a new device - Apple Support

If her iPod is an iPod Touch, it should work as long as the new iPhone is running the same iOS version or newer!than the iPod. If the iPod is running iOS 9.2.1 and the iPhone is iOS 9, you have to uodate the phone software before you can use the iPod backup.

Take a look at this support article.

Transfer content from an iPhone, iPad, or iPod touch to a new device - Apple Support

Are you sure that the iPod is backing up properly or backing up at all? On the iPod, go to Settings>iCloud>Backup>On. You should see the date and time of your last backup.

What's the iOS version of your iPod? If it's more recent than the version of the iOS currently installed on your phone, you won't be able to select the iPod backup until you set up the phone as brand new and update the phone!

Course if you do that, you'll have to wipe the phone again to restore from the backup!

Odd. The phone should be able to select that as a viable backup then. And I didn't notice that Demo already posted the information I had.

You might want to give Apple a call for additional hands-on assistance.

http://www.apple.com/contact/

I'm happy to hear that you got it all sorted out.