In the general data tab, look for "Copied Data". There are 2 boxes under that, Morph Race and Armor Race. Try setting each one to "Dragon Race" or whatever race you've tried to duplicate (For example if you try and duplicate the Argonian Race, you'll need set Morph Race and Armor Race to Argonian Race as well, it needs to match) There's a long list but Dragon Race is near the bottom of the list.
Yes I found this out the hard way myself, it is in the the Official Tutorials that a copied Race will not work without the 'Morph' buttons. As I said in another thread I was adding my old favourite Breton Warrior Race so i had to figure out what was stopping it showing in the 'Race' list when starting a new character. BTW Beth did allow for a 'custom' race in the headchopping intro, the speech has been modified to suit unknown races, so no "Breton in the Rags" or that type of comment which is good, with Oblivion it was impossible to add a custom race until the Mod Fix for it got released.