I'm sorry about the loss of your beloved dog.
Presumably vets carry malpractice insurance, meaning they know that sometime they might be sued. But the problem would be proving that the vet did something negligently, and that was the cause of the death. If the vet adhered to the usual standards for anesthesia and performed the procedure as it is always done, it's not malpractice even if the animal had a sad outcome. I've known a couple of people who lost their pets due to them being anesthetized, but they had no way to know in advance that it might happen from the standard methods. And one had a cat die after neutering, but it was because the area got infected after he came home. If your case is totally clearcut and you have witnesses that say the vet made medical errors, you might have a chance. But then there are also legal fees, and the possibility of having to pay the vet's legal costs if you don't win the case.