A puppy in the puppy walking program does not have the right of access. It has the same rights under law as a pet dog does. Therefore a property owner is more than within their rights to deny access to a pup.
Fizz is right about working dogs and dogs in training have the right of access.
Not quite true, the dog has no right of access the handler has the right of access accompanied by a guide dog. Where it gets a little vague is in the definition of a 'guide dog trainer' a puppy walker is generally not recognised as a trainer. Some states have ruled that a puppy walker is a trainer and others have ruled that they are not. In NSW they are not considered trainers. In NSW trainers are only those that work full time in training dogs.