I believe that Elizabeth Collins was from Winterbourne Whitechurch, and also that the baby was baptised there. It definitely says Father Edward Stoodley. It was quite unusual for an illegitimate child to be given the Father's surname at this time, but possibly he was already married to someone else.
However the info. is on the full version of findmypast.com, and the info came originally from the Dorset Family History Society.
regards Paco.