Maybe I'm late, but I'll reply on your question just in case this can help for somebody else. To move your domain to a dedicated server you need to register private nameservers first, if this has not been done yet. Please seee http://www.lunarforums.com/lunarpages_dedicated_web_hosting/registering_private_nameservers-t27720.0.html
on why and how this is done. Then you need to upload the domain data to the new location and check that everything works for your there. After that, change the domain nameservers to the private ones. The domain will point to the new location as the result.
Finally, if you signed up for a new dedicated plan with a subdomain, having shared plan with the main domain, you can request the primary domain change on the new plan when it is needed. This affects nothing though, and can be done just for convenience.