These Rainbow-type lorikeets are really difficult to identify, but I think you're right about this being the "true" Rainbow Lorikeet (T. moluccans), which is also known as the Swainson's Lorikeet and also known as the Blue Mountains Lorikeet!
I believe that the purple-blue belly narrows the range of options down to either Rainbow Lorikeet (T. moluccans), Red-collared Lorikeet (T. rubritorquis) or Sunset Lorikeet (T. forsteni), and the "collar" color isn't right for Red-collared, and it seems too narrow and green for Sunset Lorikeet.
