Only lines, triangles, ellipses, polygons and rectangles can be duplicated.
To duplicate a measurement you should select it (on the image, not in the Measurement Pane) with the Measurement Selection tool .
A contextual pop-up menu will appear when you click on the selected measurement with the right mouse button.
Two of the commands on that contextual menu are used to duplicate measurements:
By clicking this command a copy of the measurements will be placed over the image. Move it to the place where you want to place it, click again to leave the new measurement in the designed place.
& Rotate 90°
Works in the same way than the Duplicate command, but only works with single-segment lines drawn with the tool.