"I think we all had fun once we knew it was all safe," Hamel told Australian Broadcasting Corp. radio Wednesday.
The flight was diverted to the northern city of Darwin where the 29-year-old mother, Paramjit Kaur, from Punjab state in northwest India, and the baby were admitted to the Royal Darwin Hospital within two hours of the birth, a hospital spokeswoman said on customary condition of anonymity.
The mother was 34 weeks' pregnant when she took the first flight of her life from New Delhi. She and her first born, six weeks premature, were both well.
The child's father, Jagdar Jagdar, an Indian-born Australian citizen who drives taxis in Adelaide, flew the 1,900 miles to join his wife and child at the hospital in the early hours of Thursday morning, the spokeswoman said.
Kaur is an Indian citizen entitled to live in Australia as the spouse of an Australian. Her son also becomes an Indian citizen.