I believe these birth details:
https://stors.tas.gov.au/NI/977710
Name: F Ware
Birth Date: 18 Jul 1876
Birth Place: Tasmania
Registration Year: 1876
Registration Place: Hobart, Tasmania, Australia
Father: Henry Richard Ware
Mother: Mary Ann Ware
Registration Number: 2115
Have been incorrectly attributed to Cecelia
***Note: Mother's maiden surname on this birth record is 'Ware' not 'Gregory'
Also Mary Anne Gregory would have been aged 47 in 1876, which is (not impossible but) an unlikely age to be giving birth.
They actually belong to the child Mary Ware that died in infancy
Mary Ware (Twin)
1876–1876
BIRTH 18 JUL 1876 • Hobart, Tasmania, Australia
DEATH 26 JUL 1876 • Hobart. Tasmania, Australia
She is the daughter of
Henry Richard Alfred Ware JNR, of Lachlan Village, New Norfolk
1848–1922
BIRTH 26 NOV 1848 • Hobart, Tasmania, Australia
DEATH 12 JUN 1922 • Gladstone, Tasmania, Australia
And
Mary Ann Ware , married Henry Richard Alfred Ware JNR
1847–1876
BIRTH 19 FEB 1847 • Hobart, Tasmania, Australia
DEATH 27 JUL 1876 • Hobart, Tasmania
Refer
Mary Ware, twin, infant
Also, you have Cecelias birth as 18 Jun 1876 but the birth record you are pointing to is 18 Jul 1876
I believe Celias parents are actually
Joel Ware
1811–1897
BIRTH 8 OCT 1811 • Surrey, England
DEATH 9 NOV 1897 • Shipwrights Point, Geeveston, Tasmania
And
Eliza Eccleston aka Elleston aka Eccles Love
1844–1929
BIRTH ABT. 1844
DEATH 5 APR 1929 • Richmond, Tasmania, Australia
Refer:
Her dob on that profile says 22 May 1877...however
I can't find a birth record for her. Do we have a source for that birth date?
I can only find the burial records which gives birth Abt. 1875 ;
And marriage record which gives birth abt 1874
Celia is the informant at the birth of her nephew:
Wilfred Edgar Henderson (Parents: Richard Henderson [Sailor] X Susan Esther Ware); Informant: Cecilia A Ware (Aunt)
https://stors.tas.gov.au/RGD33-1-71$init=RGD33-1-71P691