Puppy Insurance for pets from 5 weeks of age. Essential cover for your new puppy to cover against those unexpected vets bills. Puppy Insurance cover can also provide cover for death, Public Liability and more. When looking for puppy insurance you need to decide what type of pet insurance cover you require. Their are lots of different types of insurance products available, so it can be quite confusing. Look at the different types of insurance we have in the pets section and make your choice based on your own personal circumstances.