First, you are going to need to install the application RPMs. There is no way around that.
You will need to dump your MySQL database and import it on the new server. You will need to create new userids that are the same as the older platform/instance so connectivity won't be interrupted.
Then you will need to modify the Postfix master.cf to point to your local MySQL server instance/database.
I recommend reading the following article for getting MySQL, Postfix & Amavisd working together...
http://www.howtoforge.com/virtual-users-domains-postfix-courier-mysql-squirrelmail-fedora-10