@lena It sounds like you are looking for a companion, not so much a "support animal". (relieved sigh) A Basenji might (or might not) be the right kind of dog for you. The bond between a Basenji and their owner can be quite strong. Which would probably be what you are looking for.
The shedding might not be. Basenji's shed. Their fur is quite fine, , but it's there. Everywhere. You might not notice it so much, until you do yoga on the floor that you thought was clean... and realize that your slacks work very well as fur dustmops! Breeds that have limited to no shedding typically have hair more than fur, or super tight curls. Think Maltese, Schnauzer, or Poodle.
As far as children are concerned... Most dogs will tolerate children they are raised around. Provided the children are taught how to respect the dog. You're on your own with this aspect.