Thank you for responding to my message.
On the 1841 Census Elizabeth has a son called Henry aged 7 who was born before she married Lewis Hingley. I know Henry's fathers name was Charles Key or Ley but cant find his birth/baptism anywhere. Henry was my gg grandfather and wish I could find out more about his ancestors.
After your information I have managed to find the burial for Elizabeth Hingley which was on the 11th October 1851 in Duffield.
I have also just found the baptism you mentioned and it says that Betsy was 2 1/2 at the time of her baptism on the 18th August 1811, so she must of been born early 1809, her brother John was also baptised at the same time, You could be right about the name being short for Elizabeth.
Kind regards
Janet