One way is to copy the iTunes folder from your desktop computer's Music folder to an external hard drive. Then connect up the hard drive to your laptop and run iTunes. Then drag the iTunes folder from your hard drive and drop on to your iTunes library at the top left of iTunes. Once that is done, in iTunes, Select File>Library>Organise Library>Consolidate Files.
After the copy is complete, select Store>Authorise This Computer and enter your iTunes Store username and password. Now connect your iPod. Ignore any messages about erasing your iPod and set it up to sync with the new computer. Everything should then transfer across.
There are many methods of transferring your iTunes from one computer to another. Many methods are shown on YouTube and all over the Internet. The above method is the best for large Libraries of Music/Apps/Movies etc. even if not all of it at once is ever synced to the iPod, as an external hard drive can handle a massive amount of files, also both computers do not even have to be networked together with this method.