Map a Separate Domain Name to a WordPress Page or Post

I have own two Domains: For Example...
1. - main website currently in production

On is an about Jane bio post - which has a different look and feel, and menu structure from the other pages on

What do I need to do to map my new domain - to post? I want it to appear as though it's a separate site from eventhough, it's really just a post on same site? Also, if somone goes to or they type in - either way they should see in the URL browser. Last, I don't want to come across spammy to Google. Any assistance on how to achieve this would be greatly appreciated.