I have family that left Australia (could be Sydney or Melbourne) and went to Benton Harbor, Michigan.
I can narrow down the time to between May 1919 and August 1922, more probable 1920.
They are Elizabeth MINCHINTON b.1863 her daughter Rita Sylvia MINCHINTON b.1896 and another daughter
Beatrice Ruby (Minchinton) HUDSPETH b. 1887 (probably more likely travelling under her maiden name) and her son
Roy Thomas HUDSPETH b. 1908 also known as Laurie and also could be Minchinton surname.
Passenger lists
You can narrow the date down to between June-Dec 1920. I wasn't able to find information about their trip to the US, but I did find this (see below).
New South Wales, Australia, Unassisted Immigrant Passenger Lists, 1826-1922
Name: Mrs. E Minchinton
Port of Departure: Fremantle Via Adel Melb
Port of Arrival: Sydney, New South Wales
Voyage Arrival Date: 31 May 1920
Vessel Name: Zealandia
Name: Miss R Minchinton
Port of Departure: Fremantle Via Adel Melb
Port of Arrival: Sydney, New South Wales
Voyage A