I know that most vets do not recommend that dogs go to a groomer until they've had all of their shots. Depending on when you first acquire your dog, the average dog should have all of their shots by or before 6 months.
Where I live in NJ, most grooming businesses will not groom your dog until they have received all of their immunizations. However, to groom your pup at home is perfectly fine, just make sure to plug his ear canals with cotton to prevent water from getting down the ear canals. This will prevent the dog from getting an ear infection, which is much worse than smelling bad.