Mabey a Maltese, if you keep it's hair cut short. They are very cute with short hair. My cousin has a Maltese named Bunny. She has her cut real short, they don't have to brush it and she is just a doll! I know they're nonalergenic. I don't think they are yappers. I know 2 and they r sooo sweet! They aren't yappy and they luv to snuggle. I think they are good with kids and they are one of the smalest breeds, next to a Chihuahua. A Yorkie might b good to if cut short, I don't know allergy wise though.
How about a Bichon Frise or Westie. If you keep them cut short shouldn't be too much grooming involved. They both are sturdy little dogs, about 12 to 18 lbs., they are all white. The ages in our household range from 21 to 85 and our little mix is great with everyone. We take him out to PetSmart and to concerts where there are alot of little kids and he adores them. He loves to run and play hard but he also loves to cuddle and give lots of kisses. You may not want to get a puppy but consider getting a little older dog, like a couple of years, so you don't have to go thru all the housetraining and such. Check out rescue sites and also check with your local shelter, maybe you would find an great pet there. Good luck! Forget to mention, they don't shed much at all. If I get a small brush amount out of Cody in 1-2 weeks that's a lot for him. We have friends with allergies and they don't have any problems being around Cody.
My mini schnauzers are wonderful with my children, and they are good dogs for allergy sufferers. You can also keep them groomed where they don't have a skirt and they are very easy to take care of. They are are a hardy little, yet the perfect lap dog. If you get one with a harder coat you don't have to worry about much matting if you leave skirts on.
There are a couple sites for puppy searches (not allowed to print in here) that allows you to type in what your looking for in grooming, size , coat, temerament, etc. and then shows all the breeds and standards for each, try googling dogs for sale, or dog advertisements, etc.