If you staying on the same server then you'd be better off just switching the main domain to the new one then adding the current one as an add on then a redirect. It'd be a lot easier. There is a way you can transfer everything from 1 and 2 but im not 100% sure on how to do it. Other wise just download all your FTP files and re-upload them to the add on domain's folder if your going to do that method, just be careful with the DB, the files in your FTP are replaceable whereas your DB (sometimes back ups go wrong, so don't always rely on those) isn't.
Well, if you move all the files, the config file will be connecting to your current DB, which is fine although I wouldn't use 2 domain on 1 DB due to:
1. Errors when trying to login through both domains, due to the cookie settings in ACP (there's a mod to get around this but it's not always the best way to deal with things.)
2. There's often more issues caused by having 2 domains then the time it requires to manage them.
If I were you, id change the main domain to your new one, set the current domain to a add on and redirect it to your new domain, that way you get the same traffic, same forum, same hosting account, same files, same DB and you don't have to worry about the trouble of moving your files over.