Are there any examples how to authenticate your desktop Facebook application using PyQT and embedded webkit? 
This is to provide better user experience than opening Facebook authentication page in a separate browser window.
I don't believe you can open an "authentication page" in a separate window under Facebook's terms (I used to work for Zynga, and we couldn't then, so I don't know how you'd achieve this now legally). 
Second, you're looking into the QWebkit backwards I believe. From a UI perspective this is supposed to provide access to websites, and interact with them. If you want a good looking page, with all the bells and whistle, it pains me to say it ~ but use Actionscript 3, or Ajax and it's bundle.
This post would probably be answered better if tagged in the javascript, php, and as3 sections. As the php guys will know the correct hacks to get your intended result, if possible
pyqt, webkit and facebook authentication?