There are some transcriptions on FindMyPast of Dorset baptisms, the nearest date-wise being:
Little Bredy - 9 January 1758 - son of Joseph and Jenny. 1758 via the Dorset Family History Society transcription, 1757 from the Family Search transcription.
Powerstock - 18 October 1789 - son of Thomas and Mary
Melbury Sampford baptisms on FindMyPast appear to start in 1813 - there are no instances of the surname Palmer.