Yes - this would be a nice time saving feature! ;-)

Often I need to copy a detail, shape or an entire Building floor plan to a new layer as base for the further designing.
Yes, there is a possibility to do that in QCAD but it's still a kind of workaround.

However ... if I see how easy it already is to select something and move it in the Property Editor to a different or new layer then I like to have an additional option what could be called:
"Copy Selection to a New Layer".
Maybe placed to the right of the "+" / "Move Selection to a New Layer"

What do you think?

I usually do:
Make a selection
Copy/Move
Point to reference, say point x,y
Point to Target, same point x,y
Keep Original (now the copy is selected)
Change the Layer in the property Editor
Done
This will keep all the specific properties too.

One can add an new Layer/Sublayer while the copy is still selected.