I just download the .sql file then copy and paste into the new hosts mysql database..
Do you just export it, create a new DB on the new host and import it back?..
I'm assuming you have access to the old host still since you're asking if you can just export it. You could do that but if you're running cpanel you can just transfer the whole site in WHM panel including dbs...
Cpanel on the old site, GoDaddy's gay interface on the new site..
I usually won't use anything that doesn't have cpanel, but GoDaddy is the only host with reasonable month to month and this is just some temporary side stuff that I don't want on my main hosting account. The old host I had them on is MidPhase and they are shitty...
If you're using phpMyAdmin export it as SQL without compression, which is usually selected by default, and it'll bring you to a page with a text area with the code in it. Copy and paste that into a text file..
Then on your other server, open up whatever database management software GoDaddy uses. Find a query button, it should bring you to a page with a text area - then just copy and paste the code from your text file..
It'll automatically re-create your table structure and insert all of your data...
The phpMyAdmin method works very well.
Alternatively, if you have shell access, On your current server ... Run the SSH command ...
Mysqldump -uUSERNAME -pPASSWORD DATABASE > dump.txt.
Upload it to the new server and run.
Mysqldump -u<username> -p<password> <database name> < dump.txt.
That should have you set on the new server ....
If the database is pretty big, you might want to consider using bigdump..
BigDump: The Staggered MySQL Dump Importer.