How do I make Python, QT, and Webkit work on a headless server?

If PyQt5 is an option, Qt 5 has the "minimal" platform plugin.

To use it, modify the argv passed to QApplication to include ['-platform', 'minimal'].

One of the constructors of QApplication takes a boolean argument GUIenabled.
If you use that, you can instantiante QAppliaction without an X server, but you can't create QWidgets.

So in this case the only option is to use a virtual X server like Xvfb to render the GUI.

Xvfb can be installed and run using these commands (assuming you have apt-get installed). The code in the original question is in a file called render.py.

sudo apt-get install xvfb
xvfb-run python render.py