Kitty Harry born Kapunda South Australia 1864

[Essie]

There are variations of the surname MINEAR. 
Also more than one Jane MINEAR.

Found this family with a HANCOCK connection so perhaps some 'twigs' worth researching? The Jane mentioned is a similar age to Mary HARRY.
https://www.wikitree.com/wiki/Menear-1

Essie

[maddys52]

Interesting also that Elizabeth HANCOCK (MINEAR) died at Kapunda.

There are other MINEAR/HANCOCK marriages in Cornwall as well as Elizabeth MINEAR and Samuel HANCOCK in 1843. Also Eliza MINEAR and John HANCOCK in 1852. However these marriages are all after Mary Hancock MINEAR was born (c1835). There is the possibility Mary's middle name comes from a Godparent or family friend.

[Essie]

re....There is the possibility Mary's middle name comes from a Godparent or family friend.

That too was my thinking, though I haven't found an uncle or aunt with the surname HANCOCK or DAVEY. 
But then again the father may have been a Mr HANCOCK, 15 males with that surname married at St Austell in the 1830s!

[Lazarus]

Thank you Essie and Maddys52.
I have encountered the spelling variations on Minear also the Kapunda  common to possible connections.
Furthermore there looks to be a non conformist element.
Also there was a Rev. Joseph Hancock whose daughter Kate Hancock married John Harry s/o William Henry Harry and Mary Hancock Minear.
Might that explain Hancock as the middle name?