I’m curious - did the doctor recommend a basenji specifically or just a dog in general?
It’s just that Basenjis are so high-energy, high-strung, independent and mischievous. My instinct is to say that this breed is not predisposed to therapy or support work, though of course there are always exceptions and appropriate training will play a big part in making this situation work (though obviously that would go for any breed).
I’d recommend getting a puppy from a reliable breeder who knows your situation and can make the best possible match, so the puppy can be socialized within this particular dynamic from the get-go.
That said, would there be any opposition to looking for a more therapy-inclined breed? There are just going to be way fewer unknown variables with, say, a lab or poodle, who already have an established history as successful companions to kids with special needs.