You're set. Just sit back and wait.
• beverly.dreamhost.com is the same machine as YOURDOMAIN.com will be upon DNS update. You don't need to re-upload your data, but in a week, I suggest you change your FTP settings from "beverly" to "your domain."
• You won't truly know when the switchover is complete, as it takes up to 5 days for DNS to fully propagate. For a hint, change one tiny thing on the home page that you'll see upon switchover. While you may see the new site, others might not get the DNS update for a while and continue to visit the old site.
• The hard part is email. If you're receiving email for that domain, that's a small can of worms and needs to be dealt with separately.