She is really beautiful! My Bella is only half yorkie and I've been trying to figure out what texture her hair is ever since I've had her. She started out fluffy, but as she has grown into an adult her hair has settled into being very fine, thin, and to put it mildly, quite flat.
I've enclosed a photo, I'm thinking this would be an example of very fine hair/fur? i'm sorta clueless, lol. In comparison, Rocco's hair is thick and wooly.
We let her hair ( i should really say "fur" instead of hair, as she is mixed and does shed ) to grow medium-length, trimming her every once in awhile. I do know what you mean about them looking like rats, lol but your baby has a beautiful coat regardless!