Honestly, If I was searching for a dog that would coexist comfortably with a mature male Dachshund, I would probably not consider a Doberman. Especially not a male. As Rosemary stated, Dobermans are prone to same sex aggression. It can pop out at any time. And, in my experience Dachshunds are fairly feisty and can be aggressive. This is potentially a bad combination. A mature (or maturing) Doberman can inflict incredible damage a on smaller dog in the blink of an eye, Even unintentionally.
If I may...I would suggest fostering a female Doberman, with the possibility of adoption. This way you could fastidiously observe the interaction between the two dogs and make a well informed decision.
I am not trying to be a downer here. Dobermans are my breed for life. Still, they are not Golden Retrievers or Standard Poodles (either of which I would own in a heartbeat if I wasn't so nuts about Dobes).
I guess, the bottom line is that a shedding problem would be way down my list of priorities when considering a new "family member' given your situation.
I hope this all works out for you and I would love to hear the eventual outcome.
John
Portland OR