Is this David with parents John and Eleanor on the 1871 Census Llansawell Ganol Carmarthenshire ?
John Jenkins 36 Born Llanwenog, Cardiganshire, Wales. Inn-Keeper.
Eleanor Jenkins 32 Born Pencarreg, Carmarthenshire, Wales
Mary Jenkins 10 Eleanor Jenkins 7
Anne Jenkins 5 Lellicia Jenkins 3
David Jenkins 1 Month Born Llansawell, Carmarthenshire, Wales
Sarah Jones 23 Servant.
The Welsh 1871 Census was taken on the night of 2 April 1871 which should make the birth of David more March 1871

Have you got the birth certificate for David (just to clarify) ?
RG10 Piece 5482 Folio 15 Page 9
Sandra