Duplicate Website with different theme?
You could take a look at themekey module. 


  ThemeKey allows you to define simple or sophisticated theme-switching rules which allow automatic selection of a theme depending on current path, taxonomy terms, language, node-type, and many, many other properties.


One other property is "host", which would fit into your demands, although this wouldn't be actually a copy of your site. Instead you would just switch the theme on another domain. (On a side note you should consider avoiding "duplicate content" for better serach results.)