The Qld electoral roll shows in 1905 Louisa BAKER lived at Goodwin Street Bundaberg. Street numbers are not given, but also at Goodwin Street Bundaberg in 1903 and 1905, Henry John McGREGOR, a carter.
After his marriage in 1906, the 1908 roll shows him at Park Street Bundaberg as a carter, but perhaps his wife has not enrolled so does not show.
John Henry’s half- sister, the daughter of Jesse BAKER was registered as Mabel Grace BAKER but is sometimes seen as Mary and sometimes as May.
She married in 1901 (reg 000121) Mabel Grace BAKER to Jens Peter NELSEN in QLD.
The surname was actually NIELSEN.
Jens applied successfully for naturalization in 1905 as a native of Denmark and the documents show he arrived here in 1897, and is now married with one child. He also is a carter and lives at Goodwin Street Bundaberg.
https://www.naa.gov.au/explore-collection/immigration-and-citizenship/citizenship-recordsThe son, George Henry NIELSEN was born 1902 in Qld (ref 000496)
I am not sure that this marriage was successful and I have not located the couple sharing an address. At some point Mabel Grace became Mrs Fraser.
All this is not enough to be positive, but to me it indicates that Louisa BAKER was close to her son Henry, and after her marriage to Jesse BAKER and his death, the boy remained with her in the same street (possibly the same house) in Bundaberg until he married Harriett Matilda.
Sue