Query on children of William COOK

I have found the following records
Records
* 1821 William COOK married Harriett HUBBARD in 1821 at Sydney
* 1828 census William COOK 28, Harriet 26, Mary Ann 2, Benjamin 1
* 1836 William COOK baptised 10/1/1836 at Castlereagh to William COOK and Harriot
* 1841 Elizabeth COOK born 1841 Port Macquarie to William COOK and Ann
* 1842 Charles H COOK born 1842 Montellorus to William COOM and Ann
* 1843 Frederic COOK born 1841 Cobbity to William COOK and Ann
* 1844 Ann COOK born 1844 Port Macquarie to William COOK and Ann
* 1846 Eliza J COOK born 1846 Port Macquarie to William COOK and Ann
* 1846 Eliza Jane COOK born 12/3/1846, baptised 30/8/1846 Port Macquarie to William COOK and Ann
* 1848 William COOKE born 7/7/1848, baptised 5/11/1848 Port Macquarie to William COOKE and Anne
* 1849 Christiana COOK born 1849 Cobbity to William COOK and Ann
* 1849 Christiana COOK born 3/4/1849, baptised 13/5/1849 Narellan to William COOK and Anne
* 1852 Harriet COOK died 1852 Dapto
* 1853 William COOK married Ann KEARNS in 1853 at Sydney
* 1855 Rachel COOK Born 26/12/1854, baptised 19/8/1855 Port Macquarie to William COOK and Ann
* 1857 Amelia COOK born 1857 Macleay River to William COOK and Ann
* 1867 Alice COOK born 1867 Macleay River to William COOK and Ann

https://australianroyalty.net.au/individual.php?pid=I49704&ged=...
William COOK
married Harriet HUBBARD in 1821
* Mary Ann 1826-1894 married Horatio Silvanus ROBERTS (death record daughter of William)
* Benjamin 1827-1908
* Sarah 1829-1901
* Susan 1832-1913
* Harriett 1834
* William 1836 (birth record 1836 COOK William to William and HARRIAT, death record 1837 COOK William)
married Ann KEARNS in 1853

http://familypedia.wikia.com/wiki/William_Cook_(1800-1874)
William COOK
married Harriet HUBBARD on 22/11/1821 in Sydney
* Elizabeth 1822-1823
* Ann 1825-1826
* Mary Ann 1826-1894 married Horatio Silvanus ROBERTS
* Benjamin 1827-1908
* Sarah 1828-1901
* Susan 1831-1913 married John Samuel HAYES
* Harriet 1834
* William 1835-1836
married Ann KEARNS on 18/10/1853 in Sydney
* Mary E 1839
* Joseph 1840-1904 married Elizabeth WOOD
* Elizabeth Ann 1841-1924 married John PARTRIDGE
* Charles H 1842
* Frederick 1843
* Ann 1844-1929
* Eliza Jane 1846
* George 1847
* William 1848-1935 married 1) Elizabeth GILBERT 2) Elizabeth MACKAY
* Thomas 1848
* Christiana 1849-1849
* Catherine 1851
* Rachel 1854-1895 married George Henry AVERY
* James F 1855-1855
* Amelia Fanny 1857-1887
* Matthew 1859-1933 married Frances MANNING
* John William 1861-1886
* Alice Ann 1863
* Martha 1864-1941
* Mary 1867
* Jane Alice 1867-1940 married Richard DUFFY

https://www.wikitree.com/wiki/Cook-3874
married Harriet HUBBARD 1821
* Elizabeth 1822-1823
* Ann 1825-1877
* Mary Ann 1826-1894
* Benjamin 1827-1908 married Rosemary Ann LAMBERT
* Sarah 1828-1848
* Susanna 1832-1913 married 1) William WOODS 2) John Smithers HAYES
* Harriet 1834
* William 1834-1837
* Mary E 1839-1841
* Joseph 1840-1904 married Elizabeth WOOD
* Elizabeth Ann 1841-1924 married John PARTRIDGE
* Charles H 1842-1842
* Frederick 1843-1848
* Ann 1844-1929 married John BENSON

married Ann KEARNS 1853
* Eliza Jane 1846-1927 married John BARCLAY
* William 1848-1935 married 1) Elizabeth GILBERT 2) Elizabeth McKAY
* Catherine 1851-1856
* unnamed girl
* Rachel 1854-1895 married George Henry AVERY
* James F 1855
* Amelia Fanny 1857-1887 married Andrew HYDE
* Matthew 1859-1949
* John William 1861-1886
* Martha 1864-1941
* Jane Alice 1867-1940

Looking at the children with the same/similar names as some appear to still be living when a sibling of the same name was born

Alice
* 1863 Alice Ann / Jane Duffy
* 1867-1940 Alice Ann / Jane Duffy (confirmed child of William and Ann - Alice)

Amelia
* 1857-1887 Amelia Fanny Hyde (confirmed child of William and Ann)

Ann
* 1825-1826 Ann Cook, infant
* 1825-1877 Ann Cook
* 1826-1894 Mary Ann Roberts (confirmed child of William and Harriet)
* 1841-1924 Elizabeth Ann Partridge (confirmed child of William and Ann)
* 1844-1929 Ann Benson (confirmed child of William and Ann)
* 1863 Alice Ann / Jane Duffy

Benjamin
* 1828-1908 Benjamin Cook (confirmed child of William and Harriet)

Catherine
* 1851-1856 Catherine Cook, infant

Charles
* 1842-1842 Charles H Cook, infant (confirmed child of William and Ann)

Christiana
* 1849 Christiana Cook, infant (confirmed child of William and Ann)

Eliza
* 1846-1927 Eliza Jane Barclay (confirmed child of William and Ann)

Elizabeth
* 1822-1823 Elizabeth Cook, infant
* 1832-1913 Susan Elizabeth Woods - Hayes
* 1841-1924 Elizabeth Ann Partridge (confirmed child of William and Ann)

Fanny
* 1857-1887 Amelia Fanny Hyde (confirmed child of William and Ann)

Frederick
* 18443-1848 Frederick Cook, infant (confirmed child of William and Ann)

George
* 1847 George Cook

Harriet
* 1834 Harriet Cook

James
* 1855-1855 James Cook, infant

Jane
* 1846-1927 Eliza Jane Barclay (confirmed child of William and Ann)
* 1867-1940 Alice Ann / Jane Duffy (confirmed child of William and Ann - Alice)

John
* 1861-1886 John William Cook

Joseph
* 1840-1904 Joseph Cook

Martha
* 1864-1941 Martha Cook

Mary
* 1826-1894 Mary Ann Roberts (confirmed child of William and Harriet)
* 1839-1841 Mary E Cook, infant
* 1867 Mary Cook

Matthew
* 1859-1933 Matthew Cook

Rachel
* 1854-1895 Rachel Avery (confirmed child of William and Ann)

Sarah
* 1828-1848 Sarah Cook
* 1828-1901 Sarah Cook

Susanna
* 1832-1913 Susan Elizabeth Woods - Hayes

Thomas
* 1848 Thomas Cook

William
* 1834-1837 William Cook, infant (confirmed child of William and Harriet)
* 1848-1935 William Cook (confirmed child of Willian and Ann)
* 1861-1886 John William Cook

QUERIES

* Alice in 1867 a child was registered to William and Ann Alice (on Geni as Jane Alice), therefore it would be likely that Alice Ann COOK born 1863 had died before 1867

* Ann - there are 2 children born 1825, one died in 1826 and in 1877. In 1844 an Ann was registered to William and Ann. It would seem unlikely that they had 2 children called Ann born in 1825, and unlikely that with a living child Ann they would have named another daughter Ann in 1844

* Mary - there is a child Mary Ann registered to William and Harriet in 1826 who died 1894 - it would seem to be unlikely that there would be children born 1839 and another 1867 also called Mary

* Sarah - there are two children called Sarah born in 1828 - one died 1848 and the other 1901

Can anyone add any supporting information for these children

The only place Alice Ann COOK appears is on http://familypedia.wikia.com/wiki/William_Cook_(1800-1874)

there are no sources

it includes Jane Alice COOK born 1867 - who we know was registered as Alice not as Jane Alice.

Removing Alice born 1863 until we can find proof of her.

Looking at Ann COOK

Ancestry.com TREES have the following children as the children of William COOK and Ann HUBBARD
* an Anne COOK died 1825 buried 24/3/1825 however this person died in England
* an Ann COOK born 1825 died 1913 this is sourced from 3 other ancestry trees for her sister Susan /Susannah COOK born 1831 died 1913

The only Ann COOK that I can find dying in 1877 is Ann COOK nee KEARNS died 22/7/1877 in West Kempsey