If they lived in Ruspidge then this may be a child and Annie would be the christian name of the mother < a number of ifs !! > which would be the "missing" person in freeBMD sorry :-(

Year: 1912
Month: Oct
Day: 24
Parents Surname: MORSE
Child Forenames: Arthur
Father's Forenames: Matthew
Mother's Forenames: Annie
Mother's Surname:
Place of Residence: Ruspidge East Dean Gloucester
Occupation: Collier
Officiating Minister: R. H. Woolridge
Event type: Baptism
Memoranda: U. M. Chapel Ruspidge
Notes:
Register Reference: D2598 5/6
Page No: 133
Parish_Chapel: Forest of Dean Bible Christian Circuit

You can eliminate all!
When checking the original the Page Number should read 375 and not 376
A search of marriages in March Quarter 1909, Westbury on Severn lists this entry:
TURLEY Annie Westbury S. 6a 375

A search was then undertaken of Births with Surname MORSE and Spouse Surname TURLEY and we have:
Births Jun 1912
Morse Arthur Turley Westbury S. 6a 488
Births Sep 1914
Morse Florence M Turley Westbury S 6a 510
Births Sep 1921
Morse Rowland Turley Westbury S. 6a 543
Births Jun 1922
Morse Vernon L R Turley Westbury S. 6a 518

Mike

PS Meek married Meek and Pearce married Baldiwn.