The current version of the Advisor Quiz plugin doesn’t have a dedicated import and export option. However you can use the WordPress builtin Import/Export tool that will work well, although it has some limitations.
To Export your quizzes, go to Tools > Export and select the ‘Quiz’ option from the available post types.
Click the ‘Download Export File’ and you should get a XML file that includes the information for all your quizzes.
To import your quizzes after an export, go to Tools > Import and select the WordPress Importer option.
Then follow the instructions on screen to upload your export file and import the data into your website.
In the settings page of the plugin you can also find an option to export and import just the settings for the Advisor Quiz plugin. Follow the instructions on screen to perform the export/import.