The veterinarian is doing the right thing according to New York's guidelines for veterinary practice, which you can find at (see paragraphs 5.11 and 5.12).  Not only may the veterinarian be protecting her/his own professional reputation by not prescribing without sufficient information, but she/he may be protecting your dog from taking medication that isn't advisable or optimal under the circumstances.

As the practice guidelines indicate, veterinarians are obligated to stay personally acquainted with the keeping and care of their patient by virtue of:
  1. a timely examination of the patient by the veterinarian, or
  2. medically appropriate and timely visits by the veterinarian to the operation where the patient is managed, or
  3. medically appropriate and timely visits by the patient to the veterinary facility where the veterinarian is working.

In addition, drugs should not be prescribed for a duration that is inconsistent with the patient's medical condition. The drug should not be prescribed for a period of more than one year from the date that a veterinarian has examined the patient and prescribed the drug, unless a subsequent examination of the patient has determined a continued need for the prescribed drug.  Maybe July's wellness exam (which could be called a "subsequent examination") was not intended to evaluate whether the dog still needs Prozac at the same dosage, whether a different drug or dosage might be more effective, or whether stopping treatment should be considered.

You can ask the vet's office about what kind of blood work was done at the wellness visit, and why they might need more blood work to judge the dog's response to treatment with Prozac.