What I do is, after you make the DTD, wrap it up in either plastic wrap, or trash bags, then do a whole other coat of duct tape. The plastic wrap will help separate the layers of duct tape, one being the dummy, the top being the pattern. I'll often use different colored duct tape too.
So you cut the pattern tape off the dummy, lay it out--making sure it's flat and using darts where necessary--on the fur and then cut it out, sew it up and voila! This way, you still have your in tact DTD to work off of.
Also helpful tutorial for cutting the fur: http://www.youtube.com/watch?v=gkuZ5m_yS8g