Install on second machine using same disk / Purchase a second key

I purchased the Windows 8 Pro disk from Amazon, and installed it on my desktop with a clean install. Now I'd like to do a clean install on my wife's laptop. I'd imagine I could just purchase another key and use the same disk, but can't find any option to do so.

If I choose the download option from Microsoft's site, will it email me a key before actually downloading it, so I can use my disk? Or should I just pay the 69.99 for another disk and key?

Yes, you got email with the key.
http://www.eightforums.com/tutorials/11885-windows-8-upgrade-assistant-download-run.html