Re that Qld m.c.
If we assume that Arthur’s dad was a policeman in NSW at some time in the 1860s to 1890s … then we should expect to find some indexed info at NSW State Archives
https://www.records.nsw.gov.au/archives/collections-and-research/guides-and-indexes/police-service-guideand
https://www.records.nsw.gov.au/archives/collections-and-research/guides-and-indexes/police-service-registersI have had a quick skim for Arthur O'Donnell…. But please do check and re-check…. I found ziltch… (two as O'Donnell, but not Arthur
)
I have also tried just keying in Arthur as the given name and leaving everything else blank … so that for example the Surnames are in alphabetical order for all those with a given name of Arthur ….
So the nearest to O’DONNELL seems to be :
Arthur DONNELLY
Arthur Joseph W DONNELLY
Alfred Arthur Rynsey OCONNOR
Arthur John ONEILL
Arthur OSBORNE
I haven’t searched my pre-federation NSW electoral rolls for Arthur O’DONNELL simply because policemen were exempt from enrolling as they were the ones acting under the authority of the Police Magistrates and compiling the lists of those males aged 21 and over who were British Subjects and thus eligible to be enrolled to vote in NSW elections.
Noting a birth place as Paddington, Cumberland, New South Wales on a 1892 m.c. is somewhat unusual …. I would have expected it to be recorded in 1892 as Paddington, N.S. Wales …. But I have no detailed knowledge of the Queensland Primitive Methodists Clergy’s admin rules and practices.
Have you considered searching Trove for ‘Constable O’Donnell’
JM