I think it is possible. First copy the terrain -> That is done by opening the Terrain palette and making sure that all 3 options there are unchecked (these options are: Apply Textures, Apply Cliff and Apply Height) - having any of these checked will instead apply the checked option.
Once all options are unchecked, click in your map. Then press and hold left mouse button and drag your cursor over the area you want to copy. You will see that the area is in green rectangle.
Then press CTRL+C buttons to copy. Open your map, press CTRL+V. Now around your cursor the green rectangle should appear. Select the place where you want to paste your copied part and left-click there.
Then copy doodads in same manner -> when having Doodad palette open, drag your cursor over the area you want to copy.
However make sure everything you want to paste there is already created in object editor.
I think it should work like that (I copied only parts of map into the same map at most, not in different map, but imo it should be possible)