You can probably ssh in the same way and use MySQL command line to get a copy.
mysqldump -h [HOSTNAME] -p -u [USERNAME] [DATABASENAME] > [FILENAME]
…and have a look in the wiki entry to see how to use phpmyadmin when the domain has moved elsewhere.
Opinions are my own views, not DreamHosts’.
I am NOT a DreamHost employee OK!! :@
You act on my advice at your own risk!