There are WordPress plugins that have been developed to duplicate entire sites.
You can look into one of these plugins as an option to duplicate a WordPress/WishList Member site. All WishList Member settings, members, etc. are stored in the WordPress database. So, if a plugin creates a complete copy of the WordPress site/database, it should include all the WishList Member settings, members, etc.
We have heard the plugin named Duplicator is a good option.
More details can be found in the WordPress plugins directory. There are a few different plugins available that duplicate / clone sites.
Note that we did not develop these plugins so we cannot support them.