In this video, Peter Karlsson will show how to copy objects and keep the z-value in the floor plan. 

There are two ways of doing this. The first alternative is preferable if you only have a couple of elements to move. The second is good if you are moving many elements.

• Type copy then .xy 
• Choose the point to move the object
• need Z type 0
• Second point type .xy and choose the new location
• need Z type 0
  And now you are done.
  
  The Second alternative is applied in the options. 
• Box the alternative in Options -> Drafting -> Replace z value with current elevation