Australian forward basing would signal an alliance

Could the United States shift Pacific Fleet ships to Australia for forward basing after Japan withdrew?

Only through a major agreement that would signal alliance with the British Empire; visits to Singapore would be politically easier than a permanent Australian base.

Forward basing in Australia would involve sovereignty and alliance commitments as well as sailing distance and available docks. Australia was part of the British Empire, so a standing American base would advertise a de facto alliance. The United States would need a substantial agreement, and Australia would be unlikely simply to surrender sovereign facilities without receiving something major in return. Port visits to Singapore are more plausible because they demonstrate cooperation without creating the same permanent basing commitment.