Through the magic of trackback, I found the following sites for moving an MT blog to a new server or host.
The info at elise.com is probably the most detailed. She drew much of her information from a PDF file created by someone named Russ.
I found out about the info at elise.com through a trackbacked post from Jean-Philippe Leboeuf.
This may be overkill for what you are trying to accomplish, though. If the Unix username under which you installed MT has direct read/write access to the other domain (which is a big if), you may be able to just update the paths on the Weblog Config admin page. That's pure speculation, though, as I have definitely not tried it. A relatively quick way to try it out would be to create a new test blog, post to it at least once, change the Weblog Config paths, and then rebuild.