changing itunes to a new computer

My problem may be different but I am so lost I am not sure where to ask the question. I am trying to get a new computer set up for my saughter to take to college. We transferred her itunes from our desktop computer to a laptop. I even think we did the authorize thing on the new computer. All of her songs appear on the new laap top however, when we plug the ipod into the USB port the songs do not dowmload to the ipod. It flashes DO NOT DISCONNECT but not for long and there are only a few songs downloaded. help please