by Usman Asar.
Yeap, PhpMyAdmin takes on Zipped files, but there is a format, once you go through videos, you'll get to understand whole process of shifting moodle to another server, together with (I believe I mentioned changing domains as well).
There is export tool in PhpMyAdmin as well, that though I havent used myself as I created the backup copy of Database from CPanel, but I am sure process will be the same. as my database was 42MB, once compressed came down to 640KB. so I am assuming yours will come down to same small size (20MB or even less) as apparently database is just text.