Trying to copy a layer between to images is right now unfortunately fairly difficult to do (at least the only way I managed to find). It would be nice if this could be improved so that it was obvious how to do it. :)

If you're in single window mode, the method I found is:

 1. Make the TARGET image active.

 2. Undock the layers toolbox so it is free floating.

 3. Enable "Show Image Selection" on the new layers window.

 4. Switch to the SOURCE image in the combo box that has appeared.

 5. Drag layers onto the TARGET image.

This took my a fair bit of googling and guesswork to discover.

The methods I expected to work (and tried first):

 a) Simple copy/paste. This just copied the contents of the layer, e.g. turning a text layer into a simple rasterised version.

 b) Dragging the layer from the SOURCE image, hover over the TARGET image tab to switch, then dropping it over the TARGET image. This made the cursor switch properly, but had no effect. Maybe the switching of active image breaks the state of the ongoing drag-and-drop.