You can definitely find any dog you want thru rescue with patience.

If you are dead set on getting a dog, given your specific situation I would suggest NOT going to a shelter directly, but going thru a rescue where the dog is fostered in a home/family environment with toddlers. Children are not toddlers. I can't stress that enough. If a dog is good with children it is not the same thing as a dog that is good with babies or toddlers. In a lot of ways the safest way to do it would be to get a puppy but it would also be the most amount of work.

An older fostered rescued dog is probably already crate trained, housebroken and hopefully obedience trained rather than left in a kennel 23 hours a day bouncing off the walls. I would also be looking at low energy, easy, small, good small family dogs like a havanese (they are hypoallergenic for the most part but as previous posters said each dog can be different and your allergy could be to saliva not dander which would be dog specific, not breed specific), cavalier king charles spaniels, or a pug etc.

Personally I would wait to make sure the new baby is not allergic, that could be a serious problem.

I have 18 years of professional dog handling experience and I have two dogs here, one is a foster pitbull mix and the other is a chihuahua, even with being very experienced with dogs, it is very hard sometimes. I would say waiting is the safer bet, but if you are set on it then please pick an easy, low energy breed of dog. By low energy I mean average energy not high energy sport type of dogs. Also, you can PM me if you every want to talk about specific breeds of dogs you like.