I have a couple of mates that have come from RAAus to GA (the opposite to what you want to do) and tell me you must do conversion training,either way. Both streams now go from beginner to an RPL before then going to either a PPL for GA or to RA Aus system of tack on ratings,such as cross country,controlled airspace, passenger carrying etc. A PPL therefore should only have to convert to the lighter aircraft (flying it) as you would already have the other ratings. A flying school that teaches both types would be able to enlighten you more.