To move everything just copy the MONyog data folder. This is also documented in the program documentation. Only thing you need to be aware of is that the 'host' specifier may not be valid if you use 'localhost' and similar. If you only need to move the preferences (but not server registrations copy the file “preferences.config”.
Please read the documentation paragraph on the 'MONyog database schema'. It explains everything. Am I missing something?