Remember to book your pup for their first vet check right away. About a week after their last vaccine (typically 16 weeks), your puppy can be safely around other dogs. Be sure to slowly introduce them to others, staying well away from dogs that have not been vaccinated or seem unwell. With family dogs, introductions can start when the puppy is home.Remember to book your pup for their first vet check right away. About a week after their last vaccine (typically 16 weeks), your puppy can be safely around other dogs. Be sure to slowly introduce them to others, staying well away from dogs that have not been vaccinated or seem unwell. With family dogs, introductions can start when the puppy is home.