I think you should look at QwtPlotZoomer and QwtPlotPanner. Use QwtPlotZoomer object to set the scale the same way as QwtPlotPicker does. Now you have your window. Use panner to move in the window.
Normally, QwtPlotPicker object is used to define the window in the qwt plot. Once this is done, autoscaling is switched off on qwtplot. There are innumerable threads on the the three classes mentioned. You should be able to do it.