Mark Keans, 39, has terminal cancer and is at home in Brisbane, Queensland, while his four children are in Sydney.
Queensland authorities have refused repeated pleas to grant an exemption to tough Covid-19 travel restrictions.
More than A$200,000 has now been raised after the case caused outrage.
Australia has implemented extremely tough travel restrictions to control Covid-19, including on movement between the country's states and territories.
Mr Keans was initially told he needed to choose just one child who would be permitted to see him.