Both the Hague Adoption Convention (1993) and the Hague Child Abduction Convention(1980) are in force in the United States. Both are intended to harmonize disparate legal doctrines in countries with different systems. And both are intended to provide certainty in the legal protection of children.
In U.S. practice, however, they function quite differently.
The Abduction Convention requires member states to establish procedures for returning a child to his or her country of habitual residence after being removed from that country or wrongfully retained in another country. Pretty straightforward stuff there– imagine a little girl was born in Korea, but has spent her entire six-year life in Illinois. Her mother decides to take her back to Korea– and stay there– without her father’s consent. Korea would be obliged to return the child to the U.S. pursuant to a valid Hague request. If a German mother sends her son to spend the Christmas holiday with the father in Vermont– but Dad refuses to let him go home to Germany, U.S. authorities should force the boy’s return.
If a family in Australia seeks to adopt an orphan from Italy, then permission must be sought from the Italian government via a Hague request. But if the child’s mother emigrates with her to Australia and puts her up for adoption several months later, no such permission is necessary. The child’s habitual residence changes upon the mother’s entry into Australia.
Habitual Residence. Habitual residence means that you live somewhere regularly. ... A person can cease to be habitually resident in a country in a single day if he/she leaves with a settled intention not to return, and to take up long term residence in another country.
The concept of habitual residence is not defined but is recognised by Indian courts. Indian statutes require residence as a ground for jurisdiction.
Domicile is the place where a person has fixed his ordinary dwelling, without a present intention of removal.
For purposes of jurisdiction, “domicile” means a legal residence which is the place where a person has fixed dwelling with an intention of making it his/her permanent home[i]. Domicile is a combination of two factors namely, residence and intent to remain. ... Residence is of a more temporary nature compared to domicile.
If Australian government is not treating you as a habitual resident of Australia due to the nature of visa i.e., student's visa, you cannot claim adoption even though CARA has given NOC for this adoption, because while obtaining permission from CARA you have not explained your actual residential status or the nature of visa you have obtained from Australia hence it has slipped out of CARA's mind, hence you cannot claim it as a right, because CARA is an organisation and not an authority to grant any such permission or approval especially when a country's laws do not permit you to go ahead.
You can inform CARA about the prevailing law of the Australian land and convince CARA about it.