I have a lot of friends who do this. A lot. Like, so many. And my opinion on this matter doesn't mean I love them any less.
But honestly, people. You are not your baby.
Profile pictures are for people to identify you. It's supposed to be a picture of yourself.
There are silly things like Pokemon profile picture month and that one week when people had celebrity doppelgangers as their profile pictures, and that's one thing.
I also think it's perfectly acceptable to have a couple of people or even a group of people in your profile picture.
But to have a picture of just your child and not you at all is not only silly, but also confusing.
You can have as many pictures of your child as you want on your Facebook page. Make entire albums dedicated to the pictures you have taken of them. I don't care! Just don't make it the picture I'm supposed to identify you by.