I just saw this and felt I had to reply to it. I've been in rescue for many years and worked with many dogs. Sometimes things just don't work out - you did the responsible thing by finding an appropriate loving home for your dog. It's not your fault and when dealing with small children you can't really take chances. Sometimes breed does come into play, sometimes it is just the individual dogs personality - you just never really know. I know it's a difficult thing to do- I wouldn't not ever get another dog because of it. Maybe right now is not a good time, wait until your child grows up a bit. Consider different breeds - but aside from that different dogs. Many mixed dogs are awesome with kids. If you deal with a rescue, deal with one that knows their dogs and how they relate to different animals and to children. You'll find you'll have a great deal of luck. When dogs would come into my rescue I always kept them for a period of time and put them in different situations to get to know them and what they liked/disliked. Had a ton of success in finding them the appropriate home that way and keeping them there.
I know my Chihuahua gets along with everyone, but I have no small children and he never saw one until he was 1 year old. He barks at them, chases them. He doesn't bite them but he gets very anxious when they yell and run around, he's just not used to it. Some dogs cannot handle small children, it's just the way they are. Doesn't mean there was anything wrong with your dog, or you, or your child.
I know it hurts having to part with him, but please know it's alright. Sounds like you found him a nice home, and I hope one day you will find a dog that fits in with your family. I know you'll be able to. I had to rehome a rescue dog I loved - but she wanted to kill everything on my farm. I couldn't keep her chained up because that would have been completely unfair to her. So she lives on a farm now where there are no farm animals, just her and a couple other dogs. Happy as a clam. Broke my heart - but she didn't fit here - she fit just fine somewhere else.
Didn't mean to make this so long but I want you to know stuff like this happens and the main thing is you were responsible, did the appropriate thing for the dog, and your family and took care of everything. A lot of people just abandon their dogs or would consider putting them down. You did the right thing, although it was hard, and I am confident you will have a dog again some day that fits into your family.