Quick Answer: The vet is within their rights to decline to write a prescription.
Though most Vets will write a prescription on request, in Australia, they are not obliged by law to do so. Most Vets will require an in-person consultation with the animal before prescribing, depending on the concern and vet.
If a vet is unwilling to write a prescription or the fee seems excessive, you can raise your concerns to the vet.
Suggested reading:
Asking a vet for a prescription