Can I copy music from my iPod classic to my iPod touch? If so, how?

No. The music on the Classic must be copied back to an iTunes library first. Then you can configure the iPod Touch to sync this same music content.

See this excellent user tip from another forum member turingtest2 outlining the different methods and software available to help you copy content from your iPod back to your PC and into iTunes.

Recovering your iTunes library from your iPod or iOS device

B-rock