Well .. yes – if I understand!.
Use the 'scheduled backup' feature (from 'powertools' menu). In the wizard there is an option to add a timestamp to the file name. And the ZIP option will probably be useful too. You may do so on you local machine or on the server using SJA for Linux.
FAQ links: http://webyog.com/faq/category/25/sqlyog-job-agent-sja.html