As a generalisation and without wanting to venture into legal areas, a domestic partnership is ....
.... a relationship between two adults who are not married to each other, but who are a couple (irrespective of gender or whether they live under the same roof) where one or both provided personal or financial commitment and support of a domestic nature for the material benefit of the other.
Each State has its own rules. In Victoria the Relationships Act 2008 says all of the circumstances of the relationship need to be examined.
Paid carers are not included.
Proving or not providing a Domestic Relationship is time consuming and expensive. There is no express requirement that the relationship is exclusive. This has become important for financial planners and lawyers and testators because a deceased person owes their domestic partner a responsibility to make adequate and proper provision of them in the Wills.
A tax agent often asks whether there is a joint health insurance policy to prompt taxpayers to think about this examination.