Moving the installation is very posible...
See http://www.magentocommerce.com/boards/viewthread/13826/P15/ for more information but I found that using the following in the SSH terminal allowed the domain to copied up or down the folder tree on the server
cp -fR /www/vhtdocs/folder1/magento/* /www/vhtdocs/folder1/
This make a copy of everything everything apart from the .htaccess file, in the folder above (use your own logic to flip the folder names to copy into another folder instead of out-from) which takes a few seconds to FTP down then back up, the original post regarding shifting folders doesn't mention that the .htaccess file lists a BASEHREF to the wrong folder after moving so remember to alter that... but all told it went well.
The command is 'cp (copy) -f (overwriting) R (including sub-folders) /www/...(from)/*(everything) /www/...(to)
You can then keep the old installation as a backup if you like.