What are your recommendations for a small breed that does not shed and does well with children?

I highly recommend you not get an Italian Greyhound at this juncture of your life. Physically, they are on the fragile side of the spectrum, so it wouldn't be fair to the dog to be placed in a home with a young child. Your daughter wouldn't hurt the dog on purpose, of course, but young children tend to grab, pull, and bang in their exploration of the world. When she starts walking, and for some time after that, she will be unstable and uncoordinated. (I'm a mom, and I remember those days :-D)

In general, small breeds tend to not be the best pick for a household with young kids, due to the increased risk of physical or psychological damage, but if you have your heart set on a small breed dog, I would recommend a pug. Yes, they shed, but with frequent brushing, the hair left around the house should be minimal. (And, eating dog hair isn't all that dangerous.)

More important than breed is individual personality, since there is so much variation of temperament within each breed. A good option to consider is to visit a nearby rescue organization. Mixed-breed dogs are just as good as purebred, and it can be hard to find a breeder who puts the dogs' health and welfare above their own wants. And a dog rescue is more likely to be honest about a dog's behavior (and more knowledgeable about a dog's potential) than a private party looking to rehome their dog.

Congratulations on becoming parents; enjoy the ride!

If you get a dog with hair instead of fur there will be no shedding, but you will need to brush and cut the hair. I take my dog to the groomer about every 5 weeks, and it costs 60-70 dollars each time. So make sure you want to deal with that. In my case, my boyfriend is allergic to dogs, so my little Coton de Tulear is perfect. We've had her almost two years, and no breathing problems yet.

You could get a toy or minituare poodle, shiztu, etc.

Shih Tzu, Yorkie, or Lhasa Apso mix breeds are good. They do have to be groomed though; however, no shedding. There are less medical problems with mix breeds. Have a good personality and are also so cute!

I would absolutely recommend a Maltese. As they do not shed, they need to be groomed (I do it myself, then take her in for a cleanup every 3 months or so), but very sweet natured (my daughters used to put doll dresses on ours.) The only medical issues are the need for dental cleanings (typical with small dogs) and I've heard they sometimes have knee cap issues (although ours has not.) Very adaptable and a great traveler as we have lived in both Hawaii and Germany as well as the US mainland.

I have severe allergies and have successfully owned the following "hypoallergenic" breeds: Mini Poodle, ShihTzu, Mini Schnauzer, and currently Havanese. Our Havanese are wonderful with our grandbaby and grandtoddlers. They love being part of the family. They don't shed and can be kept short. They prefer the sofa to the floor for family time. We show ours so keep them in full coat which requires frequent brushing. Havanese are small but sturdy little dogs. They don't require a lot of exercise but will have fun romping with your childen or going on walks. They are little clowns, not barkers, and will steal your heart.

Havanese hands down. Very friendly dog and perfect with kids..

Any of the above breeds are good, as long as you actively teach your children how to treat dogs (no ear pulling, pushing, poking ect) While these are friendly breeds, as a rule no child should be left alone with a dog. Gotta keep kids and dogs safe :)

It sounds like you're not necessarily looking for a hypo-allergenic dog, but a shed-free / little-shed dog. As Margaret noted, most hypo-allergenic dogs will need grooming which can be quite costly.

Big dogs can be just as, if not more, tolerant of kids than little dogs. It is their personality and trainability that you are looking for. Training is essential for any dog in a household with kids - both training for the dogs and teaching the kids to be respectful of the dog.

Look for a short-haired dog with a great personality: Boston Terrier (my favorite!), Boxer, Bulldog, Pitbull (they have a bad rap, but they can be just as friendly and gentle as a lab), etc.

Havanese or Poodle would be a perfect fit