You'll want to do a 301 redirect (permanent redirect). This points your old domain name to the new domain name while still preserving all the links you have from other external websites. By doing a quick search for 301 redirects on Google you will get plenty of info on how to do it correctly. No need to do a temporary switch over so that both work for a short time. Just switch it all at once and make sure all the proper redirects are in place when you pull the switch.