HQ,
If you don't have command line access, you can find a PHP or CGI script that will do the backup for you. Then simply FTP the backup file out to your new server.
Here is an example, it's a little much though for your needs:
http://geeklog.sourceforge.net/sampl...ackup-database
This is command line PHP, but you can change that easily by removing the first line, etc.
Good luck,
PxG