If your old domain is not live, then how about renaming the directories under which the domains are?
1) rename "new domain" directory to "empty"
2) rename "old domain" directory to "new domain"
I am not sure if Dreamhost has other ways to register where the domain is. I don't think trying this could hurt - you can always go back.
Maybe some other users can comment if this makes sense.
Not sure which plan is best? This chart lists the plans.