If your old domain is not live, then how about renaming the directories under which the domains are?
- rename “new domain” directory to “empty”
- 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.