Here's a pattern which relies on dog measurements. It may work out for you. I had trouble trying to knit a dog sweater for our Welsh Corgi. I couldn't find any online. We have the same problem with the long hot dog body and the short legs. I realized that I had made this more complicated than it needed to be. Ignoring the stubby little legs, our dog is a medium size. I believe dachshunds are small size dogs. Look for a small size dog pattern. The only adjustment you might need to make is to knit it a little longer. The neck and chest shaping should be about right on these patterns. I knit my dog's sweater in all rib to accommodate the deep barrel chest and give a flexible fit.
Good luck trying to keep it on him. lol I had to coax Ein (short for Einstein) out from under the bed with a dog treat to get the sweater on him. He hates the sweater and always wriggles out of it.