Can you only have a sacramental marriage? I have tried to find an official ruling from the Catholic Church on this matter, but haven't had any luck and have only come across others asking the same question. This question is from the angle of an Australian and therefore Australian law and marriage law.

Is it possible to have a sacramental marriage only? And not be married in the eyes of the country's law?

This question is relevant on multiple fronts: not wanting to get 'legally' married because neither of you want to combine financial assets, not wanting to get 'legally' married because you disagree with the country's marriage laws, etc.

Another aspect would be, could you get sacramentally married if you are already seen in the eyes of the country's law as de-factos? Or do you need to get civilly married regardless of your de-facto status?
The Catholic Church recognises the laws of the countries in which it is present. An information booklet issued by the Australian Catholic Marriage and Family Council  for the Bishops Commission for Pastoral Life of the Australian Catholic Bishops Conference - 'Getting Married in the Catholic Church: Frequently Asked Questions' - contains the following paragraph:


ARE CATHOLIC PRIESTS AUTHORISED MARRIAGE CELEBRANTS?
Most catholic bishops, priests and deacons are normally authorised marriage celebrants in Australia and its Territories under the Commonwealth Marriage Act 1961 and as such are legally authorised to solemnise marriages in accordance with Australian law. Note that each country has its own laws with regard to civil marriage requirements.


As well as being a registered marriage celebrant in order to perform any form of marriage ceremony. the priest must include prescribed words in the marriage ceremony and must officially register the marriage as soon as practicable. There are serious penalties for non-compliance.

In any case, why would you want to have a marriage ceremony that is recognised only by the Church and not by society at large? If you wish to maintain financial independence either during marriage or in the event of marriage breakdown, then talk to a solicitor about managing your financial affairs.