In 1871 Jane says she's 34, so maybe looking for a slightly older Jane.
This is one possibility.
A baptism at Ncle All Saints, 8 Oct 1836. Jane Miller, parents William Miller (Pitman) and Ann, of Wide-open.
A marriage at Ncle All Saints, 12 Dec 1835, William Miller and Ann Surtees, both otp, one of the witnesses is an Alan Miller.
1841 census, Hazlerigg, Weetslade,
William Miller, 25, Coal Miner, b. Scotland,
Allan Miller, 20, Coal Miner, b. Scotland,
Jane Miller, 5, Y,
George Reavely, 20, Coal Miner, Y,
Ellen Reavely, 25, b. Scotland,
John Reavely, 2 mo, Y,
Allan Reavely, 7, b. Scotland,
Ellen Surtis, 11, N,
HO107/822/6/28/14
This area appears to become Camperdown. On later census, John Reavely b. 1840 gives his place of birth as Camperdown.
Some trees on Ancestry have this family. Ellen Reavely is the sister of William and Allan Miller. Ellen Surtis is the daughter of Williams deceased wife Ann Surtees. William remarries to an Isabella, also born Scotland, and goes on to have further children, but Jane disappears after 1841.
Alan.