Because a medication like Fluoxetine takes about 2 weeks to get fully into the system, to become effective, it takes about the same amount of time to be safely removed from the body's system, when the dog no longer requires it.
Weaning slowly, by decreasing the current dosage by 1/4 for a few days, then decreasing the initial dosage by 1/2 for a few days, then decreasing by 3/4 for a few days, so the dog is left to take about 1/4 of the original dosage for a few (3) days, is the best way to wean.
Possible side effects during the weaning process, may include an appearance of the original behavior which was being treated prior to beginning the medication, and symptoms similar to those which the dog may have exhibited when the medication was first introduced. You can read more about the medication itself, below:
"A gradual weaning-off regimen should be used at the conclusion of treatment. Possible side effects include restlessness and reduced appetite. If these side effects are seen, the dose should be decreased or interrupted. Again, follow your veterinarian's directions and talk with him or her first before ceasing or altering the dosage." (source: petplace.com)
Speak to your vet before beginning the weaning process, and I hope all will go well.