Ritalin absolutely is a controlled substance in Australia and requires a psychiatrist or paediatrician to prescribe it. I've never heard of a GP prescribing it (unless they're also appropriately qualified as one of the above).
GP can prescribe it if the patient has been diagnosed by a specialist (like the psychiatrist/paediatrician you mentioned). They can't prescribe it if you have not been diagnosed. This is just so the patients can get repeats on their meds without having to see the specialists all the time.