What do you mean by "XWindow Screen"? Aren't you mixing two terms here?
I think you need to get all the lowlevel X stuff required to open an XLib window from QX11Info. Then you should be able to open the dialog. If you need to handle any X events, you can do that by reimplementing QApplication::x11EventFilter(). But be aware this window will look very odd compared to other windows in your program.
I won't help you with such lowlevel things, sorry. I don't want to touch bare XLib unless I really have to. I suggest you avoid it as well.
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