I am amazed at the responses; I just joined the community but did not expect such help.
On 30 June 1921, Stanley is applying for land for farming. He identifies as a Widower, as being 27 years old, and as having one dependent, a "daughter (1 yr 8 mos)".
The only woman I know of in Stanley's life is Mary Ann Roberts, whom he married in Aberdeen in Nov 1918. At some point in 1919, she's filing a missing persons report, "They were supposed to be going to Australia, but he has put it off, and now she doubts his background and wants it checked."
She immigrates with her family in Oct 1923. If the baby in question were hers, she would have been born in the interim, then surrendered to Stanley for him to take back to Australia. It's possible, but seems improbable. In that rare case, I can almost imagine Stanley just reporting his wife as dead for the sake of simplicity. I'm grateful for the group verifying no Scottish female birth records support that hypothesis.
The other (now more likely) option is that the daughter is the offspring of Stanley and some other woman, potentially an Australian.
To the question of Mary Ann Roberts in the USA, she is with her Father and brother in Des Moines, Polk, Iowa, USA in the Iowa 1925 Census, still identifying as Mary Sheriff. By 1930 US Census, she appears as Mary A Roberts, with mom and dad. By 1940 she has married again, US Naturalization process in Sep 1943.
Stanley records I've found just indicate he struggled in farming and dealt with bankruptcy court in 1931. Eventually probate of his will granted things to a Malcolm Thomas Brooksby (half-brother). No daughter is mentioned.
I've looked for the daughter but haven't found her. Approx. DOB per the land doc would be Oct 1919.