The intuitive approach for doing a copy&paste operation of an entire scene is by first selecting all elements (CTRL-A). This, however, will fail, as ScenePainter is only able to handle one single node in a copy&paste operation. If multiple nodes are selected, they are automatically packaged into a synthetic container.

The correct way to copy&paste an entire scene is to select it's root layer from the scenegraph dialog (STRG-G) and copy&paste that one.