there is a post somewhere by Ipstenu-DH in another thread (that I can't seem to find right now) that outlines exactly how to do this, using a plugin to update your database.
I'm not sure that you gave the correct IP to the customer. If it is for use in pointing an A-record to the site then the first thing you need to do is add the domain on the manage domains page. Then you can click the DNS link, when the next page loads look at the table of entries dreamhost created. The first one listed should be type A folled by an IP... that is the IP you need to get the customer/registrar.
FWIW, it's a much better solution to have them set nameservers to ns1.dreamhost.com, ns2.dreamhost.com, ns3.dreamhost.com and let dreamhost manage the domains. With the A record approach, it doesn't happen often, but the IP can change. If an A-record is pointed to IP address it will break the site when that happens until manually updated. If dreamhost is the authoritative nameserver for the domain, that would be fixed automatically for you.
FYI - the directions skip it, but after you add that domain, my advice is wait until you see the dreamhost coming soon page before heading to the one click installer. DNS changes take time to propagate from a few minutes to usually 4 to 8 hours... but sometimes even longer. If you've already isntalled but are getting a 404 page not found error, don't worry... just wait and try again.