Can you suggest a danderless animal companion for my dog?

There is no animal without dander. Dander is skin flakes. All animals and people have dander except aquatic animals.
If your son is having difficulty with dander why get another dog? Wouldn't that be double the trouble? Or does your dog live outside and has no contact with your son?

Is your son on medication for his allergies? It must be very difficult for the little lad to be allergic to somethng as common as dander. I guess he's allergic only to animal dander.

There is no such thing as a danderless animal. ALL animals, including humans, have dander.

All living creatures have dander.

anything that has skin will have dander.. you're out of luck there.

I think a second dog is your best bet. Two dogs are always better than one.

You don't want your son to try out a new kind of dander do you?

Frequent brushing, outside, and then one more round of vacuuming inside might help.

Are you against getting a hypoallergenic dog? Labradoodles and Goldendoodles are hypoallergenic and about the same size as a shepherd mix.

A "danderless" dog doesn't exist. Dander is basically just dead skin flakes, like dandruff (get the connection?) so any mammal will have dander. Animals excrete a natural oil from their pores (like humans) to keep their skin and coat healthy. People have a reaction to the oil on fur that dogs and cats shed and the dead skin attached to it. Pigs and dogs actually can get along rather well if the pig is used to dogs and the dog is ok with pigs. But some pigs get dry skin which can only exacerbate the dander issue. Bichon Frises, Pulis, and Poodles don't shed their fur, it actually grows like hair so there is no loose hair or skin and the dander reaction is kept to a minimum.

get the second dog but take both to the groomer every 3 weeks for a proper bath and dry this does help much

real groomers book appts months in advance so get the second dog and then in with a professional groomer for every 3 week baths

professional groomers deal with this all the time and they know the correct shampoo and brush outs to minimize allergic reactions

and just about any dog can be bathed every 3 weeks without any harm to the dog, it's an old wives tale that it's bad to bathe a dog, it's the quality of the shampoo, the skill of the groomer which is important

is your dog playful? if not, i wouldn't get a puppy until your current dog passes. Germans can get frustrated easily and could tear your pup to bits if it tries to play. An adult hypoallergenic dogs are hard to find in shelters. but try first. puppies need time so, not the best idea.

I would get a goat or a Miniature pony.