We had similar issues with our doxie. She was about 10 years old, and her back went out. She lost control of her hind legs and just dragged them behind her when she walked. The vet told us she was not in any pain (no feeling in her hind legs), and we should let her rest and keep her as still as possible. She did also advise that we could put her to sleep. We would not do that - she was part of the family. We had to carry her legs when we let her out to "do her business." She was this way for a month or so, but eventually her disc healed on its own and she started walking again on her own. We had investigated the "doggie cart" and other solutions, but rest was what worked best. Her back and hind legs went out two other times, and she recovered from both of those as well.
We did eventually have to put her to sleep last summer (she was 14). She was such a joy and we still miss her.
Good luck with your doxie.