Double-eyed Fig Parrot (Cyclopsitta diophthalma)
The bird in your picture is not a Double-eyed Fig-parrot: http://ibc.lynxeds.com/photo/double-eyed-fig-parrot-cyclopsitta-diophthalma/nice-male-sitting-perch it is another Australian Parrot, the Musk Lorikeet: http://commons.wikimedia.org/wiki/File:Musk_Lorikeet_jul08.jpg
Your right it is the one with his head turned. Please remove the picture
The one with its head turned is a Rainbow Lorikeet, the Fig Parrot is smaller than either of these.
Rather than delete the image I have moved it to the Musk Lorikeet page and you can now view it here: http://davesgarden.com/guides/birdfiles/go/1223/