The best thing is that you edit your local compueter host file and add your domain and the ip of the new web server there. If your running Windows on your local computer, then you can use the following application to simplify that task: http://www.rekenwonder.com/hostadm.htm
Remember that after you have added a domain and ip in "Host Administrator", you must close your browser completely and start it again, then you should see the site on the domain on the new server.