Moving site to a new domain name?

Hi,

I have a site live right now and I want to do a new one in WordPress. However I cannot have it down while I am working on the new site. Any ideas on how to do that? I want to setup the wordpress installation through GoDaddy and it does it automatically with our domain name. If I buy another domain name and do it there, can I move it to a new domain name once it is finished? Or any other suggestions?

Thanks!