The focus for DirectX with Qt is for exploiting the Microsoft graphics acceleration API in cases where the OpenGL support is not good enough. The easy way to do this is by using Google's ANGLE Project (the code site and the Google Gets Into The 3D Driver Game Phoronix article). The "Almost Native Graphics Layer Engine" is designed by Google for improving the WebGL on Windows experience by translating OpenGL ES 2.0 API calls to DirectX.
The discussion about DirectX/ANGLE with Qt begins here on the Qt development list.
There is at least one Qt example demo working with the ANGLE-izied Qt while other examples are resulting in crashes or incorrect rendering. Those wanting to try out ANGLE Qt can find more information particularly in this message.
As said by one Qt developer, "I'm convinced that this kind of work is really important for QML adoption since a lot of final Windows users do not have a working opengl support mostly because they use outdated drivers, and they can be hard to update, especially on laptops. The ultimate solution would be to use ANGLE as a fallback if the initialization of a classic opengl context fail, but that seems a really laborious task."