The family will now be allowed to live together in Perth while they pursue legal action related to their immigration status.
Four-year-old Tharnicaa Murugappan was evacuated to a Perth hospital last week after contracting a blood infection.
Her medical condition reignited public concern for the family's welfare.
Immigration Minister Alex Hawke said the father, Nades, and eldest child, Kopika, 6, would be flown to Perth on Monday where they can join Tharnicaa and mother, Priya.
The family has been separated for more than a week.
