Not Veterinarian related, I was a military working dog handler. So I know more than a little about veterinary care. I worked for a podiatrist for a couple years. From what the doctor said about having another doctor review, or being the other doctor to review a peer.I don't know about vet malpractice, but a threshold requirement in any medical malpractice case is having a licensed doctor review the case and agree that the evidence points to negligence on the part of the other doctor. We commoners, we laypeople, aren't allowed to sue a doctor unless another doctor approves.
A good start would be to gather as much information as you can, including all medical records and bills related to treatment, and get another vet to review them.
Unless the procedure was completely outside the norm, or the doctor has a demonstrated propensity to operate outside the norm. All doctors tend to go along to get along, and tend to cover each others back.
Unfortunately, your dog was probably dosed with an incorrect drug, or given an inappropriate dose of a prescribed medicine. In either case, proving it is nearly impossible. The technician who was responsible for the mistake probably didn't document anything out of the ordinary. A necropsy with full chemical analysis would probably cost more than any settlement.