Hello Chris
Sorry for the late response but I have been looking for Jemima Pickring/Dickring/Pickering only to find her name was Pickin/Picken/Picking so have only just started looking for them.
Jemima married in Stockport Cheshire to a soldier named Thomas Beard 03.06.1799 the LDS has her as Dickring. They went on to have 13 children all baptised either at Donnington or Albrighton.
Jemima died after the 1841 census was taken and was living at Albrighton however it recorded both her and her husband as from the County but then on the 1851 census Thomas recorded he was from Longhope Gloucestershire,so didn't know then whether Jemima was from the county or not. it's been a nightmare. However there are no other Jemima's with a similar name spelling. I have a copy of Stockport parish register and it is written as Pickring not Dickring.
With regards to her brother Thomas Picken he was baptised at Donnington 21.07.1782 and was recorded aged 88 on the census 1871 living with his son Henry who was born in Brewood in 1820 (I think his baptism was recorded at Penkridge).
Thomas is on the 1841 census at Brewood so he should have his wife and some family with him I would think.
There was another Thomas Picken born at Newport Shropshire 15.02.1776 father John and mother Jane. Newport Shropshire is about 20 miles from Donnington.
Joseph and Mary parents of the Donnington Thomas and Jemima also had a Uriah Picken baptised at Donnington 06.03.1774 but he died 13.07.1774, there was also Lucy Picken 28.05.1775 and although I haven't managed to find a burial for Joseph a base born child to a Mary 20.05.1787.
Thomas and Jane Pickin had 7 children all baptised at Donnington but none were named John. Joseph was the eldest so I am now looking for a Thomas circa 1725 with a possible father of Joseph.
Hope this helps

Eileen