Acquiring the proper immunizations for your puppy should not be delayed at all. There a host of illnesses and ailments that afflict your puppy and proper immunization will help prevent these problems.  Consider keeping a notebook where you can record all of the illnesses, treatments and immunizations that your puppy has had.  Consult your veterinarian for the appropriate schedule for your puppy's vaccinations.

The time that your puppy should first be vaccinated varies from breed to breed and even for different litters.  The earliest you'd want to immunize a puppy is about 5-6 weeks, but some puppies won't receive one until about 15 weeks or so.  You really should consult with a veterinarian to find the proper course of action.  Also, consider the window of susceptibility of your puppy also.  this is the time that your puppy is still susceptible to a disease or illness despite receiving an immunization or vaccination.