Hi ..
I think for your iBook it probably has iTunes version 9.1.1 installed. I can still download content from the iTunes Store on my iBook G4 running v10.4.11 with iTunes 9.1.1 but it's slow going even on a high speed broadband connection.
If by chance you are using iCloud on your iMac, you won't be able to sync iTunes content to the iBook. iCloud's minimum requirements is v10.7.5.
If you move music from the iMac to the iBook, make sure there's enough free disk space.
Control click the MacintoshHD icon on your desktop or open the Finder, right or control click startup disk in the Sidebar on the left then click Get Info.
You'll see Available and Capacity. Make sure there's at least 15% available disk space.