Looking at that 1871 census,
John Bray 70 b Cornwall
Elizabeth 40 Daughter single b Cornwall
Richard 21 occ Shoemaker b Cornwall
my guess would be that Amelia was the daughter of the unmarried Elizabeth, and named her maternal grandfather as her father when she married. There were several common practices for children of unmarried parents who named fathers when they married -- often combinations of their stepfather's name and occupation, their biological father's name and occupation -- and naming the maternal grandfather was definitely one of them.
It's possible that her father was a John, just not a Bray, and that he was a miner.
In 1871, she is called "daughter", and Ancestry has interpreted that as daughter of the head of household (which is how relationships were supposed to be recorded). It likely means daughter of one of the other household members. In 1881 she was called "niece" of Richard Bray, and his sister Elizabeth Bray is in the household, so this does suggest she was Elizabeth's daughter.
You left out one person from the 1871 census:
Sarah, unmarried, 29, born Chasewater.
She was also in the 1861 household, 18 and unmarried, and is a potential mother as well.
And in 1861, just for example, there is a John Sanders, aged 19, copper miner, practically right next door.
And I see that as I was typing, Keyboard86 also suggested the obvious.