I think it's POSSIBLE for a Yorkie to live peacefully with a toddler. But it's not something I'd really WANT to do.
I have a sister significantly younger than me. She was not even a year old when I brought in 9 week old Jackson (keep in mind: he is a bigger Yorkie, was already 5lbs by this age). I still live with them and it works, they really love each other, but it's hard. If she were my kid, I am not sure I could have handled both. Good news is that she's not my kid, LOL, she's my sibling. So she's all my mom and stepdads work
She's in daycare Tues-Friday until 5pm and they often go to dinner, or do their own thing, etc... if I had my own child AND had to raise Jackson as well, I would say I would have been really really really stressed.
Emma, who is now almost 4 years old, is still learning every day. I wouldn't trust the two of them alone together. She tends to like to hug him, which he doesn't really appreciate. And very in-his-face, touchy-feely. I am always there to supervise and luckily Jackson is a very well rounded socialized tolerant dog, but I never allow him to be tormented, etc. It's a lot of work when it's the two of them together because she really loves the dog and wants to constantly play with him, but the same feelings aren't always shared by Jackson.
Anyways, long story, but it's not something I'd advise. I'd wait for a few more years for any dog, personally. It's different when you already have a dog and a baby is born. Doing it the other way around can be really hard.
Also, every kid is different. My little half-brother (dads son) was always really good with animals. I would never have an issue leaving Jackson with him, though he's now almost 8. But at the time I got Jackson, he was a little over 4, and even then was always really good, quiet, calm and respectful of the animals. He just wasn't so much of a rough-and-tumble type kid as my sister is.
So I think each situation is different. Accidents can happen no matter what. But in your case, it sounds advisable to wait until your child has matured a bit and maybe learns how to properly treat animals.