I have found it to be very simple if you're moving a whole Joomla! implementaton and leaving your database in place to simply zip the entire Joomla! directory (at the root, or at a sub-level) and use DH's net2ftp to upload and unzip to the new domain. That gets every file and keeps permissions and paths intact.
Because net2ftp has a 7MB file size limit, you usually have to repeat this procedure several times to get everything if your site is large.
Then, as you noted, go into the admin panel and config files to make path changes, and you should be all set.
One thing you'll want to check for, though, is dead links in content (articles). If you used full paths rather than relative links in your content anchor tags, you will have some work ahead of you. This can be quickly resolved, if you're familiar with editing SQL exports, by simply changing the links in your database files and then reimporting the SQL dump.
To paraphrase Elmer Fudd, "Be vewwy, vewwy careful" when you're editing SQL exports!
Also, for those who may be considering creating sites "live" in a sub-directory and then moving them later, try the Joomla Stand Alone Server (JSAS) at jsas.joomlasolutions.com -- it's wonderful for local deployments if you don't have your very own Apache server to work from. Once you get your site tweaked the way you want it, you can simply copy the files over to your domain space.
Oh -- one other suggestion: I use the one-click install and have DH deploy Joomla! for me at the new location before I start the move, just so I can continue with the one-click upgrades later. You just have to make sure you're working from the same Joomla! version on both sides. And, if you mark your config file read-only, your "move" routine won't overwrite it -- so you're all set!