Yes, but it needs some back and forth pacing. Also, if custom doodads are involved you need to have them in your map.
Just go to the terrain pallette, make sure to have any tools un-selected, drag the cursor over the area you want to copy (It should form a green square) press CNTRL+C then open up the other map and paste it. You need to have the tiles of the terrain you copied, otherwise it'll just be dirt.
And then do the same thing with doodads, except do it with the doodad pallette, drag and select, copy, paste.