It appears from comparing the census data - identifying siblings - and the death certs confirm that Julia Jenkins was the dau of Sam Simpson and Jane Brewer. Her brother Ben's death cert lists Jane as 'Rebecca Jane Brewer' - don't know if that helps. Also, census data list approx birth Month/Year for Sam and Jane. Maybe that will help in your search.
Good luck - all from familysearch.org
US Census, 1880 Beat 14, 18 And 25, Jackson, AL
self Samuel Simpson M 25 SC
wife Jane Simpson F 24 AL
dau Josephine Simpson F 8 AL
dau July Simpson F 6 AL
dau Martha Simpson F 1 AL
U S Census, 1900 ED 116 Precincts 14, 17 Wells, Plevna, Madison, AL
https://familysearch.org/pal:/MM9.3.1/TH-267-12393-91096-79?cc=1325221&wc=MMPJ-4P8:n434988303
head Sam Simpson M 47 b abt Aug 1853 SC married abt 1871 29 yrs
wife Jane Simpson F 50 b abt Aug 1850 AL 8 children: 6 living
dau Ada V Simpson F 10 AL
son Ruben Simpson M 19 AL
son Ben A Simpson M 16 AL
son Charlie N Simpson M 8 AL
Texas, Deaths
https://familysearch.org/pal:/MM9.3.1/TH-267-11094-144008-14?cc=1320964&wc=13012571
Benjamin A Simpson
death 23 Aug 1969 Harlingen, Cameron, TX
Male White 84 years
birth date: 10 Aug 1885 Plevana, AL
Married Farmer
spouse's name:
father's name: Samuel Simpson
mother's name: Rebecca Jane Brewer
occupation: Farmer
place of residence: Precinct #4, Harlingen, Cameron, Texas
cemetery: Lyford Evergreen
burial Lyford, Texas 25 Aug 1969
Informants: Bessie Simpson
https://familysearch.org/pal:/MM9.3.1/TH-267-11830-88484-78?cc=1320964&wc=13012866
Ada King
Death 25 Oct 1924 Wellington, Collingsworth, TX
Female White Marrie
death age: 35 years 15 days
birth date: 10 Oct 1889 Ala
father S P Simpson birth Ala
mother Jane Brewer birth Ala
Informant: E R King
cemetery: Wellington Cemetery
burial 26 Oct 1924 Wellington, TX
Alabama, Deaths
https://familysearch.org/pal:/MM9.1.1/JK33-LKS
Julia Ann Jenkins
death 13 Mar 1938 New Hope, Madison, AL
Female
age at death: 62y 8m 21d
est birth 1876
spouse: Joseph N Jenkins
father Sam Simpson Mother Jane Brewer
