Add an HTML5/CSS3 writer. Someone seems to have started work on this: https://github.com/eegg/docutils-html5-writer.
The new html-base writer generates output conforming to HTML 5. It is intentionally using only elements also valid in XHTML 1.1. (The output conforms to XHTML 1.0 (transitional), as it uses the "start" argument for enumerated lists not starting at 1 which is not allowed in XHTML 1.1.)
Its default stylesheet "html-base.css" defines the necessary layout using CSS 2.1 rules (for better compatibility with older viewing agents). Of course, users can use CSS3 in custom stylesheets.