Hi yul, Welcome to Basenji Forums!
There is no dog breed that is truly non-allergenic (not allergy causing) because all dogs produce dander (shed skin cells), saliva, and urine. You can be allergic to the dog dander, dog saliva, or both. Urine is less of a problem since dogs usually potty outside.
Pet hair itself is not an allergen, but it can collect dander, dust, and pollen.
To answer the question about shedding, Basenjis do shed, but its not as much as some other breeds and they keep themselves very clean with their own grooming methods. Their coats are so short, though, with you'll hardly notice if they shed.
Basenjis are known to supposedly produce less dander than other breeds, and many people who are mildly allergic to dogs can tolerate some of these "low dander" dog breeds with proper environmental controls.
Be careful though, as there are no guarantees. People's pet allergies vary greatly. Severe pet allergy sufferers may not tolerate any dogs at all, even with the best environmental controls.