The American innovation on English Constitutionalism was that there is fundamental law - expressed in the constitution - that cannot be ignored by the executive and cannot be statutorily pasted over by the legislative. The Americans called them natural rights and entrenched those political rights in their federal and state constitutions.

Where an English judicial had to be activist, the American judicature could be constructionist. The English judicial established Habeas Corpus as accepted practice through activism two hundred years before it was legislated in 1679. The American judicial had a series of ongoing and increasing 'rights' laid out in fundamental law for them to protect from executive and legislative over-reach.

Despite having 130 years to digest and deliberate on the American innovation Australia did it half-arsed. Ingliss-Clark had a bill of rights in the first draft of his Washminster constitution, but this was taken out apart from a protection for religious freedom. Consequently the constitution has not been able to inform judicial doctrine like it has in the United States. So we get a half-arsed and often seemingly arbitrary judicial doctrine that gives tips of the hat to the English style of executive/legislative dominance and at other times the American style of fundamental law. (more)
Robert G. McCloskey argues that for the judicial branch to be constitutionally complete it must establish in "theory and practice" the doctrines of: judicial independence, judicial review and judicial sovereignty.

Judicial independence is well established through English law practices and hasn't been an issue in Australia. However, one draft of the Australian Constitution by Samuel Griffiths placed the judicial under the power of the legislative, rather than being independent. That unwise relationship was removed at the next constitutional convention.

Judicial review is the doctrine whereby the High Court has the power to "refuse to enforce" an unconstitutional law. This leads to the doctrine of judicial sovereignty where a "law may be held unconstitutional if the Court thinks it is, even though the case may not be plain" and the Court's decision is binding on the other branches of government.

There are other issues surrounding these especially in constitutionally based liberal democracies and republican systems. The presence of a constitution means the government is based under the doctrine of "limited government' and has competing components of 'fundamental law' and 'popular sovereignty'. (more)
Cam Riley: South Sea Republic. Freedom, liberty, equity and an Australian Republic.