This is strange, there is a record for John on the first line of page 5, same date of birth, baptized two years earlier. John is my 3GGF.
I read William's dob as Augt. 27th 1818, other 5's on the page have a horizontal bar at the top whereas the 8's finish with an upward slanting flourish.
Ah well I was hoping to find Elizabeth but it was always a long shot. I'm very thankful that you looked this up for me, I would have had an itch about it that I couldn't scratch otherwise.
There is enough other circumstantial evidence that Elizabeth is their daughter but it's always nice to have a definitive document.