Down syndrome is technically known as Trisomy 21. Humans afflicted with Down syndrome have an abnormal duplication on the 21st chromosome.
Humans have 46 paired chromosomes and dogs have 39, so the answer to your question is no, there is no "known" Down syndrome Per Se in the canine species. However, your vet may have used Down syndrome as an example of a genetic disorder that your dog may have to help explain some of her problems. There are 100's of other genetic/inherited problems in dogs, and one of them could mimic a Down Syndrome-like pattern possibly.
The following is a great article from "The New York Times" about genes and genetic diseases in dogs that you may find helpful:
Lastly, I am curious to know what problems your Rotty has to bring your vet to that conclusion. Is your Rotty a slow learner, etc? Please post again if you like so that we may be able to help you further.
First she is absolutelly terrified of humans. Which in itself is probably more common than I think. My other four Rotties were potty in less than six weeks.(no rubbing the nose thing in this house!) but PeeWee took 14 months to potty train. She runs into walls and furniture, also trips over her own feet. When I could not figure out just what was wrong with her, the vet told me that there is a form of downs that dogs can get. Don't get me wrong, she is a joy. I have a friend who has a baby with downs and she is the most precious baby you would ever want to meet. Everything is a new adventure for her. It's the same way with PeeWee. She even has the almond eyes of a downs baby. I would not trade PeeWee for anything in the world, she is a joy. Just waking up for her is an adventure. But, if this is not downs, I would really like to know what it may be. Have I mentioned that the chewing that puppies do had not stopped yet? It's like she just does not get it. I understand this, because of the potty training, but I have gone through five comforters in a year, and because they are king size, you can imagine the money she's going through just for fun. If I knew just what was wrong with her, then I could possibly find a new approach to getting her to understand.
Having been a veterinary technician specializing in critical and emergency care for six years, and working with a veterinary neurologist, I hate to contradict a veterinarian BUT, there is such a thing as canine down syndrome. Down syndrome can affect every mammal as it is defined as an extra copy of the 21st chromosome.
So... Your vet is most likely correct. It expresses differently in dogs than humans as the spinal cord connects directly to the back of the brain bringing signals in and then relaying them directly out again. It is most commonly noticed in puppies because the symptoms are most noticeable.
The common ones are:
Clumsy movement and ambulatory irregularities.
Inability to learn simple commands due to lack of ambulatory ability and poor eyesight and hearing!
From what you've said here - your Rotty is indeed a textbook case of canine down syndrome!
She probably lacks the nervous system control that housetraining requires and just took longer to develop it than usual due to the disease. Poor vision explains running into walls, etc. And as far as tearing things up and being fearful, if you could not see or hear well, do you think you would react similarly? Use baby gates to keep her away from the comforters, pick up after yourself, and that will improve. She needs routine and lots of positive interaction with people to get over the fear.
Hang in there, rotts are still pups at 14 months. By 3 or 4 most people barely notice the deficits and many dogs live longer lives than usual with this disease.
I hope this helps and when it comes to vets, trust your instincts, if it doesn't feel right, ask for a referral to a specialist. They are more open minded and won't hesitate to open a book, or call a mentor when faced with hoofbeats that may indeed, not be horses, but zebras.
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