The Gtrain Kurgo dog backpack is an acceptable carrier for a Dachshund. It's less harmful to their spine than many other dog carrier backpacks on the market because a dog can support themselves by sitting on all fours, and shift around to make themselves comfortable, although it's still not ideal.

Personally, I would not use a backpack to carry a Dachshund who is in active recovery from IVDD and would limit use in all cases to less than 2 hours at a time. If your hike or walk is longer than 2 hours, let your dog walk themselves, if possible, for at least 15 minutes and then put your pup in the backpack again. If your Dachshund is actively recovering from a disk rupture, I suggest using a dog stroller instead.