ajc, the best way to do it would be to download it onto the other computer. As long as you're not running both computers at the same time for actual tournament use, you should be fine. I say that due to some people test layouts, settings, etc on one machine while run the actual tournament. If you're looking to convert over to another computer, still download it on the other computer, enter your key, and from there, it's as simple as transferring the files over to the other computer.
Now I may be wrong on a point or two, but from my understanding of other posts, I believe that what I said would be true.