In the old days, this kind of job would be a multi-step DTS (Data Transformation Services) transaction, where you would run a SQL script that backed up the database, then ran a shell command to FTP the backed-up database to the new server. On the receiving server, you'd have another DTS job to check for a new file received via FTP in a certain folder - once the file exists, you'd then run a SQL statement to restore it.
This functionality is now handled by SSIS (SQL Server Integration Services) from SQL Server 05 onwards and requires Workgroup Edition or above (won't work on Express). I'm not too familiar with it, but
MSDN's comprehensive online reference guide should be a good place to start. Failing that, looking at replication (which you can find details on via the above link) would be the other option. Bear in mind your test server has to be Internet-facing for any such solution to not require manual intervention at some stage in the transfer process.
Hope this helps.
codegecko