However, this protection only lasts a few weeks so they need regular vaccinations from an early age. Puppies are typically vaccinated at eight and 10 weeks, kittens at nine and 12 weeks, with an initial course of two injections. Your young pet should then be given a booster 12 months after their first vaccination.Rabbits need regular vaccinations too.uppies are typically vaccinated at eight and 10 weeks, kittens at nine and 12 weeks, with an initial course of two injections. Your young pet should then be given a booster 12 months after their first vaccination.