Hi and welcome to YT. It sounds like you are on your way to being a great dad to Gia.
Hot Rod was all of 1.57 lbs when he came home to us. I was a total wreck handling him cause I thought he would break.
Hubby had to to do the honors of bathing him for the first couple of times. He did it in the hand sink with the bathroom door closed and the heater going. (Our bathroom is cold and we normally turn the ceramic heater on when we shower in the wintertime). I felt more comfortable with him doing the bathing as his hands are much larger. You may also want to run some towels thru the dryer just to warm them up. Hubby did use the blow dryer on a warm setting and ran it over him very quickly to dry him off.
Hot Rod had very sparse hair on the top of his head at this time also. It looked like he had a bald spot as well. It was just that his hair was so thin and his hair was already changing-he had the beginnings of a white spot going on.
We used Bio Groom puppy shampoo. As a matter of fact, I still use it around the face area and my 2 are 4 and 3. Yes, yorkies can have allergies, but don't look for them before it happens. It will drive you nuts. lol There really is no way to tell until your little one starts to have symptoms.
Hot Rod was 15/16 weeks when we got him and he was already flakey. It took several months and 2 vets before we were given a medicated shampoo and conditioner that help tremendously. As it turns out, he's allergic to chicken so I suspect that had a lot to do with it also.
Also, for brushing teeth, you can also try gauze on your finger so she can get used to it if a brush is too big.
Best of luck to you and Gia. Can't wait to see pics.