You could mirror, but Dreamhost’s plans allow you to host an unlimited number of domains on your plan, so there really is no need to do that.
I suggest just going to the registrar where you registered the new domain, and set the DNS entries to be:
then, go to the Dreamhost Control panel, select Add a Domain, and enter the new domain name.
As soon as DNS propagates, you will be “good to go”.
(All this is covered, rather thoroughly, in the DreamHost Wiki Just read carefully the section that describes your circumstance).