Nah, that plugin allows you to clone a post or page, or edit it as a new draft.
To back up your site, basically you need to do two things:
- Backup your database(s)
- Backup all of the assets (e.g. images, theme files etc.)
Let's start with point 1.
You can either do this by loging into your hosting company's admin area and using whatever functionality the offer you (probably PHPMyAdmin)
Or, installing a plugin, such as this one, which will do it for you.
You might also want to read: http://codex.wordpress.org/Backing_Up_Your_Database
After that, the easiest way to get to your files, is to connect to your webspace, via FTP, find your root WP folder (it will contain folders such as "wp-admin" and "wp-content"), then just copy this to your local PC.
If you don't have FTP access for whatever reason, there is a plugin that claims to do it for you.
You might also want to read: http://codex.wordpress.org/WordPress_Backups
And that's it.
Personally, I do both of these things by hand, so I can't recommend the plugin as I simply haven't used it.