Changing domain, same hosting

At the moment my domain redirects to my host. http://www.tracymorter.com redirects to http://tracyandjon.fireflyinternet.co.uk/blog/
it’s a pain as google hates me for it.
I now have the details from my host so I can use my domain name properly now.
I’m confused what to do. I found this http://www.tamba2.org.uk/wordpress/move/ would this be the right thing to do?