Hi there,
This is more of a domain name issue, and it also depends on your hosting environment (does it allow multiple domain names?).
Firstly, you ensure the new domain name is pointing to the same location as the current one. You will need to create the necessary records in your domain name server (dns) settings and ensure your hosting environment is ready to 'accept' the new record. If you are able to do this, loading the new domain will load the default DNN setup that you have made ready.
Next, login as the host/superuser account and edit the portal alias by adding the new domain name. This way, there should not be any downtime and both domains will be loading exactly the same website.
Try it out and post any problems you may face so we can help you out along the way. Cheers!