There's no point in creating a singleton -- once you call setPath on QSettings it's retained for the life of the application.

What you should do is call setPath with /Settings and then do something like this:
settings.beginGroup("Debug");
settings.setValue("size", win->size());
settings.setValue("fullScreen", win->isFullScreen());
settings.endGroup();

This should get you exactly what you want. QSettings are also very cheap to be created on the fly.