Family law does not fall cleanly into state or Commonwealth jurisdiction
The Commonwealth may legislate only on the matters that the Constitution provides and their power is: exclusive, meaning that the states cannot legislate on those matters; concurrent, meaning the states can legislate on those matters, but Commonwealth law prevails in any inconsistency; or referred, meaning a state has voluntarily surrendered its legislative capacity on the matter to the Commonwealth.
Marriage and divorce is a concurrent power under Section s51(xxi) and s51(xxii) of the Constitution.
De-facto relationships are a state power because the Constitution does not mention them, however, 5 states have referred their powers under Section 51(xxxvii), Western Australia being the exception (because WA always marches to the beat of its own drum).
Child protection generally is a state matter; however, the Commonwealth can legislate where it intersects with marriage and divorce.
The same is true of property matters.
The powers of State and Federal courts
The High Court of Australia is the top-tier court in both the Commonwealth and State hierarchies under Chapter III of the Constitution.
Other Chapter III Federal Courts including the Federal Circuit and Family Law Court of Australia do not and can not have State jurisdiction as decided in New South Wales v Commonwealth  HCA 17 (The Wheat Case).
However, State courts can have Federal jurisdiction granted to them under s77(iii) of the Constitution but only if they comply with the limitations of a Chapter III court and only if their remit is limited to the exercise of judicial power or powers incidental to judicial power. This excludes state tribunals and limits the functions that the States can confer on their courts to ensure that they remain "judicial" and do not cross over into executive or legislative power. The Commonwealth has conferred Federal power in state courts under s38 & s39 of the Judiciary Act 1903.
Additionally, either type of court may rule on State or Federal law applying to the same facts providing the primary dispute is one that falls within their jurisdiction.
Which courts handle divorce and related issues like parenting plans?
So, having established the broader picture: where do I file?
If you are married
You must be an Australian Citizen, live in Australia and regard Australia as your permanent home, or ordinarily live in Australia and have done so for at least 12 months. If you live in Western Australia, you file in the Family Court of Western Australia (FCWA); if you live anywhere else, you file in the Federal Circuit and Family Court of Australia (FCFCA) in your state or territory of residence.
If you are in a de-facto relationship
You must live in Australia and regard Australia as your family home, or ordinarily live in Australia and have done so for at least 12 months - if you live elsewhere you cannot use Australian courts even if you are an Australian citizen for de-facto relationships because, even though the powers have been referred, these are still state or territory powers and there is no concept of state or territory "citizenship". Again, the FCWA for Western Australians and the FCFCA for everyone else.
Since the merger of the Federal Circuit Court and the Family Court of Australia, complexity does not enter into the filing decision although, as I understand it, it was pretty much a distinction without a difference anyway.
Appeals follow the appropriate appeals chain: to the Federal Court and then the High Court for FCFCA, and the WA Supreme Court and then the High Court for the FCWA.