When I copy/paste the object on the left, it gives me the object on the right. I don't want that, I want it to duplicate exactly. I am trying to move it from one layer to another.

In case you are using Inkscape on Mac OS X, I'd recommend to read this Inkscape FAQ:

• Copying and pasting in Inkscape creates pixellated images instead of copying the vector objects

… and/or various earlier topics here in the forum, e.g. 'Re: Mac Snow Leopard?', and some additional details in 'Copy/Paste in MacOS with X11 - question on known bug'.

Thank you. I am indeed on OS X, which I should have mentioned in the original post, but you were smart enough to figure that out.