Setting the drag mode as Rubberband drag, you will only be able to select items based on the selection.
To implement the zoom based on rubberband, u will need to implement ur own rubberband.
For this u need to catch the mouse events in scene or view. Based on this, once u get the rectangle after rubberbanding, u just nee to call fitInView() function.

I will check if I have a pseudo code. I had implemented the rubberband zooming in one of my application long back.