I don't know whether to put this one under England or Australia, since it bounces back and forth and I have questions in both places. With such an unusual name, he's pretty easy to find, but there are a few unanswered questions in his life, nonetheless.
Dawson Gascoigne (sometimes Gascoine or Gaskin) was born, according to the censuses, any time between 1833 - 1836, probably in Earsdon, Northumberland, but some records say "Halliwell" (which I assume is Holywell, near Earsdon).
In 1841 he is with his family in Chester-le-Street, Durham, all born outside the census county.
In 1851 they are living in Murton Colliery, Easington, Durham, all coal miners.
In 1861 we find them in Ryhope, Durham, first on the page the household of Dawson's brother James, with their widowed mother also in residence, then, in the same house or next door, Dawson as head, with a wee daughter Mary Gascoigne, age 4, born Hetton-le-Hole, Durham. He is listed as married, but no wife in sight, nor can I find a marriage for him.
On 11 July 1865 Dawson, having aged a few years according to the passenger list, arrives in Melbourne from Liverpool on the Ocean Empress.
In February 1872 he marries Josephine Boland in Ballarat, Victoria and claims he is a bachelor at the time. (Josephine was born in Bolton, Durham, so they might possibly have known each other before, but she is too young to have been Mary's mother.)
One child, Quinton John Boland Gascoigne, is born in 1873.
By 1881 Dawson is back working as a well sinker, in Brotton, Yorkshire and "unmarried"
In 1887 he dies in Durham.
As far as I can tell, Josephine and young Quinton go on living happily without him in Victoria.
Question: Would there be any divorce records that early, assuming he did actually divorce? Or any record of a legal separation?
Possibly the distances involved just allowed such as he to disappear into another world, only seen "on one page" now by us, in a general search.
Back to his daughter Mary, whose line I am trying to trace:
In 1871, when her father was in Australia, she is found as Mary Gaskin in Ryhope, Durham, as a domestic servant in the Green family.
In 1873 she marries John Harron in Gateshead District, Durham. From then on I have her clearly until her death.
The problem is, I can't find her birth and don't suppose that her mother's name would be on the marriage cert, since normally only the father's name is given in England.
Since I can't find a marriage for Dawson, I have no clue who the mother might be. Quite a few Mary's born around the right time and place!
All the best,
P.S. Yes, I realize from googling that there was a famous cricket player named Dawson Gascoigne Harron, born in Durham, who is undoubtedly a relative of these people somehow, but I haven't yet figured out how - it's obviously a few more generations down the road.