Roboman,
I do not know the exact answer to your question "Is there any way I can download the key with FireFox.....?" In reality what you are doing is executing the order process using the browser; the PK is emailed to you in a conventional email. So the question is, "Can you execute the ordering process using Firefox?" I don't know, but I'm sure the MS staff will know, so keep an eye on your post for an answer.
It is very, very difficult to remove Internet Explorer from Windows XP; in fact some Windows functions are really powered by IE. So my thought is that while you may think, for whatever reason, that IE is no longer on your computer, I think that chances are it's still there and can be used to do the ordering. What makes you think that IE is no longer available to you?
Normally the ordering process begins by the user clicking on the WGA Notification icon or prompts, then follow the prompts or menu selection of "Get Genuine." At some point you transition from the installed WGA Notifications utility to IE, which takes you to the ordering pages.
