Changing Primary Domain on WordPress

I have a request from a client to set up a wordpress website. He wants to put it on a hosted site (godaddy), and he wants to use his existing domain name. No problem, I know how to change the records.

He also wants his old site to stay operational until the new one is complete. Which means I have to use a different domain name then switch it at the end.

What issues will this give me with wordpress? Is it even possible, or will changing the domain name crash the site?

It appears at least permalinks are going to give me a problem.