URL Transfers?

Hi I am wondering if i have a site url now that is in use..  Can I build a new site with dolphin using a new url and when it is complete shut the other site down and transfer the old url to the new dolphin site?  If so what is the best way to do this.  My problem is i started a site and can no longer edit it the way it needs to be edited.  So i am going to build a new site using dolphin with a new url and need my site to continue to operate untill I have the new url dolphin site built..After the dolpin site is buillt I need to transfer the url from my site now to the new site dolphin site and delete my old site.  Obviously the new url will be hosted on a server and the old one is on a different server.