Hmm. Francis is buried in Brisbane under the name of Francis Law:
http://www.brisbane.qld.gov.au/commu...arch/index.htm
and married Elizabeth Mauch (the name of the wife given in the Ancestry trees) in Queensland in 1923, also under the name of Francis Law.
So either the people with the Ancestry trees have got entirely the wrong person, being misled by his mother's name of Elizabeth Arabella Barnett in the death index, or Francis dropped his surname for some reason before he got married.
Arabella Barnett isn't a particularly common name, so I'd be inclined to think it's the same Francis, but I'm not sure you can go much further without certs.