Ctrl+C and Ctrl+V should work, while in the Path tool, directly on the geometry (points, segments, regions). If pasted while not using the Path tool, or when the Path tool is working with 0 or 2+ selected layers, it should create a new Path layer (with default fill and stroke) with that geometry.

Ctrl+D should also duplicate the selected geometry in place, as if the user had copy-and-pasted it. Currently, Ctrl+D duplicates the whole layer while in the Path tool, so this should override that while this tool is active.