There's phantomjs for that. Though I've actually had the most success with perl's WWW::Mechanize::Firefox and a headless X server.
If you insist on controlling webkit through javascript, you can use gnome-seedjs. But this is problematic/annoying because there's no commonjs implementation yet.. in phantomjs you can require() node modules in the outside context. Not so much in gnome-seedjs..
Also, X means it's not actually headless, even if you're using xserver-xorg-video-dummy or xvfb. For this reason, phantomjs got rid of the X requirement a number of versions ago.