I've seen people using normal Qt labels as FPS counters over their QGLWidget - should work as long as everything in front of the GL scene is realized as a X window/Win32 window I'd say. No idea how that works with translucency though as that maybe would require a compositing window manager.
Well, or:
http://www.qtcentre.org/wiki/index.php? ... ith_OpenGL - let Qt draw everything with OpenGL. looks like it does what you want. No idea about webkit though, should be possible however.
And no idea about msvc, never ever used that with Qt, I use MinGW/gcc everywhere.
EDIT: Oh, and you probably won't get anything as nice as your current frame loop - basically you would override the repaint method of your background widget, and then invalidate that window again when you are done - or use a periodic timer.
EDIT2: void QWidget::showFullScreen() - Qt does not have any function to set the screen resolution before that though.