I'm tempted to say the new item should appear as close to the 'duplicate' control as possible, so users see the results of their change as they click the button without relying on peripheral vision. That would mean that for your example, the new item should appear at the top of the list.
However, putting the duplicate control at the top is probably not the best method anyway - I would suggest letting users right-click to duplicate, then adding the new element below the old.
Anything's better than adding the item to the bottom, though, because with lists that exceed the size of the container, new items will either be out of view or force the entire list to scroll (these sorts of tracking animation are very distracting in peripheral vision and take more attention than a transition like this ought to).