Hi and welcome to iLounge.
Firstly, it is possible to just transfer the purchased songs to the secondary computer using any
type of portable storage medium, or even over-the-wire across a network connection. The tracks are just files with a .M4P extension, and you can import them into your iTunes library as you would any other media file.
need to authorize the other computer before you can actually play
any of them, but that's fairly straightforward also: Just select Store->Authorize Computer
from within iTunes, and enter your iTunes Store userid and password.
If you want to use your iPod to transfer them, then you simply have to set your iPod to "Manually manage my music and videos" in the "Summary" tab within iTunes (connect the iPod, select it in the left-hand source list and you'll see a "Summary" tab in the main panel... Look for the option labelled Manually manage my music and videos
, put a checkmark into the box, and click the "Apply" button in the lower-left corner).
Once the "Manual" mode is set, this travels with the iPod, so when you connect the iPod to your laptop computer, it will remain in manual mode. You can then just drag-and-drop any tracks you like onto the iPod manually -- it will not attempt to automatically sync the iPod once the "manual" setting has been enabled.
Once you've dragged the purchased tracks from the laptop onto the iPod, just connect it back to the desktop computer, and choose the "Transfer Purchase" option, as described above. Note that if the purchases on the laptop were made with an account that isn't already
authorized on the desktop, you'll need to authorize the computer for that account before the purchases will transfer.
You can find some more information on manual management in our Beginner's Guide to Filling your iPod
, and more information on transferring purchased tracks back (and even non-purchased tracks) in our iPod 201 article, Copying Content from your iPod to your Computer