Assuming the music is in your iTunes library, sync it to your iPad Mini. If it isn't, connect the device that has it to your computer, open iTunes, then go to File>Devices>Transfer Purchases. This will transfer any purchased apps, songs and other media to your iTunes library.
The only problem is iTunes does not see my mini to load things on. My mini is 16 and my iPad lg is 64 first gen. I had to delete a lot of things off the mini as it was loading. Don't care if the mini is backed up, as it is for travel.