Both my babies got their rabies shots but cannot remember how young they were . . I did not have a negative reaction on Tiger so I was never concerned when it was Annika's turn.
If you plan to take Kalina to the groomer though they will require one so if you don't intent to have her groomed by others, you should be okay
I am sure a lot of experienced breeders or Yorkie Moms can give you better advise.