Pregnancy and nursing take a lot out of a new mother, and proper nutrition is important for getting her back into fine form. Vitamins play an important role in your dog's health, but supplemental vitamins are usually not necessary for a post-pregnancy canine diet if she's eating right.
When your dog was pregnant and nursing, she was eating for the whole gang. Your vet likely recommended changing her diet to one higher in protein -- perhaps one suited for puppies -- to meet her extra needs. As well, she probably ate more. Her increased nutritional needs didn't end with childbirth; the nursing dog needs to eat increasingly more food up to a month after giving birth, as her puppies eat more. However, more food doesn't mean more vitamins. If your new mom is eating a balanced diet, she should be getting all the nutrition she needs for herself and for her babes while she's nursing. Giving vitamin supplements without veterinary oversight comes with potential dangers. WebMD notes too much vitamin D can depress a dog's appetite, cause muscle atrophy and harm bones. Excess vitamin A can cause joint pain and dehydration. If you're unsure about your dog's nutrition, talk to the vet.