buckworks - 1:25 pm on Nov 29, 2010 (gmt 0)
The fact that the other domain is so new suggests the possibility of a technical quirk.
Here's something to check: Do they have the same host as you and does your site happen to have the same IP address as theirs? And, does your domain happen to be the default for the IP?
Sometimes if someone points their DNS at their host but haven't actually set up their site yet (or they used to have a site but took it down), their domain can end up showing the content from the IP's default site.
If that's what's happening, nothing has actually been copied, but the content shows up on more than one domain. Edits made on your own site will show up instantly on the other site too. (Check for that.)
If that's what's happening, it should be easy for your host to fix. It's weird when it happens but it's usually an accidental situation, not someone trying to hurt you or steal your content.
If, on the other hand, the other site has deliberately copied your content and reproduced it elsewhere, then yes you'd have to contact their host and take DMCA action.