Looked into webkit source code. Web Inspector implemented with C++, JavaScript, CSS and HTML.
Apparently, all this compiled in one libQtWebKit.so
The only way i can imagine to modify qwebinspector behaviour is to add/redefine some its JavaScript methods in runtime. But i doesn’t know how to evalute JavaScript in the context of WebInspector…

Maybe you should ask this on WebKit forums, I don’t think you can do this over Qt without making modifications/extending WebKit source…

P.S.: If you find something, please let me know, I’m interesting in that too…