Dear Harry
It is definitely not a Square-tailed Kite, becuase it is missing a number of important features that are obvious to the trained eye.
See my gallery of Square-tailed Kite here for comparison.
http://amatteroflight.com/gallery2/v/ausbirds/hawks/sqtkt/
As Chris Sanderson suggested it is a dark morph Little Eagle, of which I have a photo, but not of the standard I’d put on my website. 
If you want I can send those to you privately for comparison.
A good book I’d recommend for you and your friend is Field guide to the birds of prey of Australia by Dr Stephen Debus, which has fantastic illustrations and photos of Aussie raptors in flight.
Regards Akos
