The OSG is built for multi-threading of osgViewer View's in various ways, it's not general multi-threading support, it's designed specifically for a scene graph so overheads for that multi-threading to a minimum.
The multi-threading that osgViewer provides is managed by osgViewer itself so it can marshal all the tasks and synchronization correctly. Doing the threading a synchronization externally should be possible with limitations to work similar to how osgViewer works, however, it won't be straight forward. My recommendation would be to work with the VSG's existing threading.
If you want to attempt to do all the threading yourself via Qt then personally I'll need to step back and let you get on with it, trying to do it work suck too much of my time, for something that might not work out, and would be of little general benefit to the community, and I have no Qt expertise to guide the process.