I would like to get my daughter a new ipod because she is having minor issues with her current ipod and the screen is cracked. She has informed me that she will not be able to transfer or save her current pictures and music on a new or different ipod. Is this correct?
iPod touch
If the pictures are in the the iPod Camera Roll album that are included in the backup that iTunes makes. Thus just restore from backup. See:
iOS: Transferring information from your current iPhone, iPad, or iPod touch to a new device
Synced items like apps and music are not included in the backup. Thus you need to get those in your/her iTunes library. See:
Recovering your iTunes library from your iPod or iOS device: Apple Support Communities
Transfer pictures/music to new ipod
