I think it is great that you are checking things out
before making a decision to breed your dog. Here is a good guide to go by -- the YTCA code of ethics and code of conduct.
http://ytca.org/frame_index2.html
I think most would think it is
not the best decision to breed an unregistered dog. She is also too young. The second heat, 18 months and over 5 pounds is generally recognized as what is safe for the Mother, who otherwise meets breeding criteria. Some females that weigh less than that can get an okay from their vets for safe breeding. The weight itself is not nearly as important as the size and measurements of potential birth canal and other health considerations. A thin, larger bone structured dog can more safely have puppies than a fat, tiny-boned one. Many 4 pound females safely have litters.
You should also review the Yorkshire Terrier standard and determine if the dogs meet the criteria. Then it is helpful to have a person experienced in judging Yorkshire Terriers evaluate the dogs to see if they are good representatives of the breed. We all love our little ones and think they are the cutest ever -- but that does not mean they should be bred.
Both dogs should be tested for infectious and hereditary disease -- appearing healthy and carrying dangerous traits that could be passed on are quite different. While at the vet, get his/her take on the physical safety of breeding your girl. Some females, even in standard, cannot safely be bred.
Natural childbirth can be great, but what happens if the pups grow larger than your female's birth canal? They won't be able to pass without killing her. So, are you prepared for C-section? Do you have a couple of thou saved aside in the event of trouble? That is not uncommon with Yorkies, especially small females.
No one should breed dogs without copious studying! You need to know what to do. As you already heard, whelping big dogs like labs is nothing like our little toys! I have been reading for several months and am no where near ready. I won't breed until I feel I am. Since mine are still puppies I have lots of time. My first AKC registered Yorkie female turned out to not be within standards, so we spayed her and loved her as a pet only. We are very hopeful about our little Sadie!
So far everything is looking great. But I won't know for a few more months. Just letting you know all this last part so you understand not all dogs, even if they were registered should be bred.
You do have a pretty little girl there! But I would look into spaying her.