I have done this numerous times on various GD accounts and have never had an issue by just exporting the db using phpMyAdmin and the default export settings, that is:
- start phpMyAdmin
- select database from the left side panel
- click the Export tab
- Export Method: Quick - display only the minimal options
- Format: SQL
- click GO
- the .sql file starts downloading
At the new hosting account:
- create a new database
- start phpMyAdmin
- select the new db from the left side bar
- click the Import tab
- File to import: click
Choose file, navigate the downloaded .sql file, select it, click Open
- leave all other options as-is
- click Go
- as long as your exported .sql file is under the Max file size indicated in the File to import section, the db will import in " a bit" :)
The only time I have had an issue is moving a site with a very large exported file. I have never had success using any of the compression methods, so I just set up the new db to accept remote connections and then use NaviCat for MySQL to do the job. This has successfully worked for db exports exceeding 2GB (eFront LMS sites).
Cheers!
Lyle