How do I get my music on my iPad onto my iPhone?

You could use iCloud and your music will be available on both devices.

I think I have iCloud set right because my photos go to both devices but not music.

You have to sync the both iPhone and iPad with the same iTunes library on the same computer. Then sync your iPod to ensure that all the music on the iPod is also on the computer, then when you plug in your iPhone, go to the "Music" tab and pick which albums, artists, playlists or genres you want to have copy onto the phone.

iCloud. Simple and very helpful.

Yeah you can set iCloud to download the music, apps and other documents which are installed on your iPhone to your new iPad. Just go to the Settings and choose iCloud.