I have done migrating my users' mails to new server. dbmail saves all mails into database (in my case mysql), backing up and restoring should be trivial.
1. backup (using mysqldump)
~#mysqldump -u user -pPassword dbmail > dbmail.sql
~#mysql -u user -pPassword dbmail < dbmail.sql
Voila. It's done!.
I have users' preferences and address books saved in database too. So the method of backing up and restoring to the new server should be the same.