Also, if you are really considering a quaker, make sure it's legal in your state. I live in Pennsylvania, and they are illegal to own here.
I have a 3 year old and a baby due in a few weeks. My house is full of activity. We have a nanday conure, lovebird, white capped pionus, and a rose breasted cockatoo. My daughter was taught not to touch the birds, and she does listen. She's at the age where we'll allow her to hold one supervised, but she gets too nervous. When she was born, I also had a hahn's macaw. I would never have let him near her, as he was a biter. But that's an individual issue.
Our most fun bird to watch is our lovebird. He's got a HUGE personality. Close second is the cockatoo, but he's a bit bigger than what it sounds like you're looking for. By far the most gentle is the pionus. She is sweet and content to just sit. She hasn't been home long, but we've had her since May. I'd trust her with the kids before any of my other birds. Again, this is an individual basis as they are all so different, bird to bird, not just species to species.
My nanday is 11 years old, and he's LOUD. I wouldn't recommend him, but as he gets older, he's becoming better around children, too. He keeps to himself but does dance and beat box with my daughter.