I think it's completely possible! It takes patience, training and diligence on the owners/parents part.
I do think it's advisable to get a pup who is going to be on the larger side though, as I think it's worrisome no matter how gentle the child is, to be living with a 2-3lb dog.
Jackson is my 16lb boy, so I don't worry too much with him. He's sturdy, but still fragile in a lot of ways too. I live with my sister who is now 4 1/2. She was under a year old when I brought 9 week old Jackson home. The two have grown up together which I think has helped. He is much more tolerant with her than strange children... he loves kids in general, but definitely prefers a quiet gentle kid.
Now I must say, my sister is a wild one. He ignores her when she's jumping and down, or running around the house (or sometimes he runs along with her) and they have a mutual respect that he wouldn't have with just some random child coming in the house and doing the same thing. She's not necessarily a "gentle" child, lol, so we had to TEACH her how to be with Jackson. And they make a very cute pair. They totally have a love/hate relationship... Emma can get frustrated if he doesn't do something she wants him to do, and he can get irritated with her pestering him, but overall things run very smoothly and they are just like good friends.
Must say though... I'm glad she's not mine and it's not us 3 together 24/7! When they were both younger, it was a lot of work when I had just her and him and nobody else to help. I like being able to give her back!
Now that they are both a bit older (he will be 4, and she is 4) it works out very nicely.
Here they were in 2011: