The original domain is registered at GoDaddy, and has proper DNS settings pointing at DreamHost. Your new domain is also registered at GoDaddy and also has proper DNS settings pointing at DreamHost.
If you created a Fully Hosted Domain in the panel, then you’re off to a good start. Since it’s a Joomla site, it’s a fairly involved process to just copy it over it to the new place. You have two choices:
Use the One-Click installs and build it from scratch and try to import your old database. Or keep plugging away at your installation and tying up loose ends in the configuration files. It looks like you’re taking this second approach.