My Suzi is 5 1/2 months old. She just had her completion of vaccines on Monday. AND Rabies. Suzi slept for a while when we got home, and was FINE. But, she does weigh 7.5 lbs.
I was very concerned about the shots too.
Since your Yorkie is so tiny, I would wait till at least 6 months old. Or , have the rabies shot given individualy. Do not let the vet pressure you to have them done all at once. I would be really worried with such a tiny Yorkie to have everything done together.
If you decide to just have one shot done, then pick the Rabies shot, because of the strict California laws.