Before i answer, I must add a disclaimer: any dog can be great with children, and even if the breed standard says the breed is not, you will find people who tell you differently. I am sharing personal experience of the most common breeds I saw turned into the shelter when I worked there for not being great with kids. I know these are generalizations and I am not trying to start any type of fight. However, these are the ones I saw with the most issues. With a very young child in the house, I would stay away from the the smallest of the small breeds, like chihuahuas, poms and Yorkies, as these little dogs can often learn that being picked up incorrectly hurts so they nip in response and then get put down. They learn to nip before being hurt and will become reactive to children. Dachshunds tend to have back issues, sometimes caused by children picking them up incorrectly or being dropped. They are top of the list for bites. I am not a fan of min pins around kids, just because they are so energetic and strong willed. I am not crazy about Lhasas and pekes with kids either, just because neither one is especially patient.
Now for breeds I do like with kids, miniature (not toy) poodles tend to have a fun sense of humor and are trainable. My first choice would probably be a bichon, as they are usually sweet and biddable dogs. Cavalier King Charles spaniels are great, but have lots of health problems. I like Italian Greyhounds, but they are very fragile, so if this is a look you like, possibly consider a whippet instead. Beagles have a great personality and love kids, but they can be barky and difficult to train or call off a scent. Some cocker spaniels are great with kids, as would be a cockapoo or other small poodle mix. I love Havanese, and they love to learn tricks. Shi Tzus are pretty nice, but can be stubborn and lazy. Honestly, make a list of what all you want out of a dog and then go meet some to see if one clicks. Be patient and don't settle.
Toy Poodle! I have a toy poodle, almost No shedding, almost odorless! Super friendly to all people including kids.
I also wanted the same characteristics on a dog and found her through http://Petfinders.com She had been posted by a rescue group in our area. She is a fantastic dog . Great personality, friendly to my cats, other dogs and people. She seems to be a mix of three different breeds.
Dachshunds are awesome and pretty docile little critters in my experience. Also, my sister has a rat terrier/chihuahua mix, with some training (they tend to be barkers, or yippers to be more specific) she is now a little guardian of my 6 and 8 year old nieces!
Poodles, shihtzu, clhuahua, ...have had each and mine all love children....personally, in your sitation, i would go with a lab.
Shih Tzu! So loving.
Grew up with Cock-a-poos. I'm 57. I married my "Only Big Dogs" loving husband 17 years ago. He thought this breed would be a lap dog. Mine is 16 lbs., non-shedding/hypoallergenic, fantastic with Grandchildren, other dogs, a hiker, adaptable, SMART, trainable. He is in love. So fun! Highly Recommend!