Sync two iPods with one iTunes library
Regardless of the kind of iPod your daughter has, you can add songs to her iPod by connecting the iPod to your computer and dragging the songs, playlists or library to her iPod. After it is finished syncing, it will be ready to go. If the iPod was previously synced to another computer and not set for "manually manage music", syncing with the new computer will replace the songs on the iPod. If the iPod was set up for manual management,  you can drag songs to it from the libraries on different computers.