As far as registration goes, you can just log into Impulse on the laptop and download and install the game with no issues. You won't be able to play multiplayer between the two computers since currently it needs a unique account for each client, however it sounds like that's not what you're trying to do anyway.

Woohoo!  Thx

If your new computer is the same OS as the old one, you can right click on your installed game on the old PC and select archive. Then copy over that archive to the new PC, install Impulse on the new PC, and use the restore archive option from the main dropdown in the top left to install directly from the archive you made. This only works if the two PCs have the same OS, otherwise you'll have to re-download.