The US citizen may apply for an Australian partner visa to live and work in Australia. Dual citizenship is possible if eligibility requirements are met, though US law does not formally recognize dual citizenship.
A US citizen remaining a US tax resident must file US taxes on worldwide income and report Australian-sourced income and foreign assets to the IRS. Professional tax advice is recommended.
Children may have citizenship options from both countries. Legal counsel can clarify passport eligibility and travel regulations.
Property, inheritance, and parental responsibilities are governed by the laws of Australia, the US, or both. Seek legal guidance for specific circumstances.