I want to use Graphviz + Doxygen to generate a class diagram based on C++ code. This works already as Doxygen comes with a native DOT suppo
Try Doxygraph!
Doxygraph is a collection of tools to automate reverse engineering UML class diagrams from your project's source code, and present them as interactive web apps.
It relies on Doxygen to parse your source code and create an intermediate XML representation of the information it collects, so it supports all the same programming languages that Doxygen supports: C, C++, C#, Objective C, Java, Python, PHP, Tcl, D, IDL, VHDL, and Fortran.
You need to read the README from the cloned Project.