Just thought I'd give an update on what I think I've worked out with everyone's help.
I now strongly suspect that Arthur O'Donnell was born in Hobart, Tasmania, on 18 Nov 1874 (not Paddington, NSW, in 1868). He was registered as Arthur Lovett son of Mary Lovett (nee Row and later Mary Balwin) with no father recorded.
I believe his father may have been the Daniel O'Donnell mentioned in this snippet from the 1868 Tasmanian reports of crime: "Mary Lovett, charged with leaving her children at Latrobe without means of support. ... Supposed to be in company with Daniel O'Donnell, late District Constable."
This Daniel O'Donnell was a convict transported to Tasmania in 1850 for assault with intent to ravish Jane Jack in Inverness-shire while a private in the 27th Regiment stationed at Fort George. His native place was County Donegal and he became a police constable in Tasmania.
Mary Row seems to have been the daughter of another convict, Mary Maguire/Mary Roe/Jane Roe, who came from County Tyrone, married, was widowed, had two illegitimate children, was transported to Tasmania in 1848 for stealing a gown, married John Hendrick (a ticket of leave convict) in 1849 in Launceston and died in the New Town Pauper Establishment in Hobart in 1885.