Another option, since DreamHost allows shell access, is to use mysqldump.
mysqldump -u <DB Username> -p<password> -h mysql.mysite.org dbname > dbname.`date +%Y-%m-%d`
The above will place the database dump (backup) in a file tagged with the year, month and day of the backup. With the date listed in this order you know when the backup was made and you can sort by filename to get backups from oldest to newest.
This simple command along with a cron job can be used to automate backups of your database. If you are already performing backups of your site off of DH, you just need to place these files in the proper location to add them to you backups.