Vaccinating a nursing dog won’t provide any benefit to her puppies -- in fact, it could end up doing the mother harm, though any problems are usually minor. Most often a vaccine may simply make her feverish or ill for a day or two, and she doesn't need such stress to her body during this time. You can vaccinate a dog while she's nursing, but generally you don't. Exceptions exist.
If a dog's nursing puppies, the vaccination shot may temporarily affect her ability to nurse as it saps her immune system for a day or so. Associated discomfort may make her irritable or otherwise cause stress for her, and it will affect the pups, if only by disrupting their feeding.
Despite any concerns associated with giving a nursing mother any kind of vaccinations, if she a shelter animal with unknown history, it’s generally best to go ahead and vaccinate her. While it won’t save her pups if they are exposed to anything new, it will help the mother and give her immunity to some of the diseases she can encounter. For dogs not in high-risk environments, it’s generally best to wait until the puppies are weaned before vaccinating her. At any rate, administering vaccines, to a nursing dog or otherwise, is best left to your veterinarian.
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