For our allergic son saliva and dander set him off so this routine seems to help: dog not allowed on any furniture (but has his own dog beds in the house), not in the child's room at night, small hepa air filter in child's room for days when the dog may be in there, a large hepa filter in the living room to use when we do any "deep cleaning" of the house stirring things up. A bath for the dog every 2wks, clipping every few months, allerpet put on after a bath and spritzed on in between baths, dog taught not to lick people. Vacuuming more than we did previously and with the bags that made for allergens has helped quite a bit with the cleaning day sniffles.
Being a large, clumsy lot a small underfoot dog was not a choice in our minds. We looked at the soft coated wheaten terrier-kind of hyper, boxy body, long hair needing to be clipped an from what we read originally bred to be farm dogs / good with livestock. We also looked at standard poodles since we had one as a pet previously and knew they were smart, energetic and quick to adapt to new rules/situations/tasks. We ended up with a re-homed 1yo standard poodle with issues about being left alone, those are resolved and now he is a great dog with the children and the chickens. He chases off the squirrels and blue jays when they go after the girls scratch, herds the girls out of the vege garden back into the free range area when they sneak in and has an absolute *I think not* bark for the hawks that fly by for a look now and then. My spouse thinks he is a genius for knowing the difference of who to chase/who to protect but I think he understood my simple whisper of "dirt nap" when he first met the chickens.
I do think it is prudent to research the purpose of a breed and would tend to avoid ones with a strong prey drive/instinct to begin a search. I understand the search for the type of dog "less likely to trigger an allergic reaction" and many of those are usually not farm dog choices. I also believe that some dogs are enigmas within their breed (?genetics/environment/training) and you might find the one that will work for you that is usually ruled out for being around small farm animals.