I know this is an older thread, but ideally since Uniform Server Zero is portable, you should not have a problem in migrating either the database or the site using a copy paste.
However, that being said, the better way to do it would be to use a fresh install and move only the items you need, i.e., the web application itself and the database.
Web Application
The PHP code is generally stored in either the www or the ssl folders, so these folders would need to get moved to the new installation. You can overwrite them without a problem.
Database
From Uniform Server, use the MySQL->Database Backup function to backup your database, this will create a .sql file in the db_backup_restore folder. Copy this file into the db_backup_restore folder in your new installation and use MySQL->Database Restore to move your backed up database file back into the database.
One caveat here. If you have any functions or routines that were created, they may have to be created again, I have seen some instances where they dont get transferred over.
Start the servers and the application should now work.
Also do you have any absolute paths in your PHP code for file uploads etc? Those will need to be changed as well.