Your adrenaline injector expires at the end of the month indicated on the device.
You should allow enough time to make an appointment to see your doctor/nurse practitioner for a PBS authority prescription and to take the prescription to your pharmacy.
Remember that the pharmacy may not have the adrenaline injector in stock and may need to order it in which may take a couple of days.
It is best to start the process of getting a prescription in the middle of the month the adrenaline injector expires in case there are any delays.