change header image for single page, twenty eleven

I’ve just about finished building a site for a friend and he’s asked if it’s possible for a particular page to have a different header image from all the others.

I currently have a twenty eleven child theme with light customisation and randomly selected banner images.

I will also need at some point to figure out how to point a domain at the same specific page. I’d find it easy on a normal php site but I’m relatively new to WP