Excellent question Barbara. The WordPress exporter only exports content like pages, posts, navigation menus, products and items like that. It doesn’t include any settings or even widgets.
So there are two options for you here. You can either move everything over by hand. That’s a bit tedious, but it’s also not technically hard and is also free. The other option is to use a backup plugin/service to copy the site, database and all, and set it up as your staging one.
BackupBuddy is a paid plugin, but it works really well at exporting and importing sites/moving them. That’s basically what you’re doing here. Some of the other plugins do make backups, but they don’t have an import tool to go with them so you’d have to manually add the database in your web host’s admin and then change the site and admin URL’s in the settings table of that database. It’s a bit more technical, but it’s less error prone than copying the settings manually.
Some web hosts also have built in staging sites. It’s one of the many things I like about WP Engine. There is a button in the admin to copy the site to staging and another one to copy from staging to live. It makes testing and development much easier.
Hope that helps out,
Bill