Found this little thing riding on my hat making a buzzing noise. Tried to take a photo and it flew off to go and sit on some grass type plant. It remained very still both initially on the hat and then on the grass. At a guess I think its not a bee, maybe some kind of hover fly but I really had 0 idea how to class it and therefore where to look.
It has only one pair of wings, so you are quite right. It is a fly. I am not sufficiently familiar with bee flies to suggest a genus, but you might find something similar if you search for images of Bombyliidae.
This tangle-vein fly is rarely recorded (there are only 3 records in the Atlas of Living Australia). It parasitises grasshoppers so maybe you can hire yourself out as a grasshopper impersonator or is that iminsectator?