These are usually given as a combination vaccine (gives protection against several different diseases) and your pup should have three sets of this combination vaccination, given at 3 week intervals. The Rabies shot is usually give at around 14 - 16 weeks of age.Puppies are extremely susceptible to many serious, contagious dog illnesses while unvaccinated. Several of these can kill a pup very quickly. It is also illegal to have a dog who isn't vaccinated against Rabies.hese are usually given as a combination vaccine (gives protection against several different diseases) and your pup should have three sets of this combination vaccination, given at 3 week intervals. The Rabies shot is usually give at around 14 - 16 weeks of age.