Aurenescia is what I used in my CoHE TL. I also called New Zealand the Austral Islands.
My so called "Australshire", which I agree is a bad and illogical name, includes Indonesia as well, so maybe a which comes from that, such as Nusantaria.
the only way the british are going to get the indies is when they later on steal even more colonies than they did otl.
the dutch and the portugese were active in the area long before the british, so if they do take it over there would already be an established name.
(of course a even bigger british colonial empire will mean it will implode even faster)
A general note - being a continent, the name of TTL's Australia will not contain the word NEW nor the suffix SHIRE.