I do not know what research you have done already on this family but it would be useful to fill in gaps, to maybe find clues to the origins of this family
Colonial Tasmanian Family Linksbirth Joseph BROOKSB. 1844 LauncestonThomasAnn ASHTON
Sa BIRTHS 1853 4/213 Elizabeth Ann BROOKS Thomas BROOKSAnn ASHTONAdelaide
1885 6/255 Fanny BROOKS Thomas BROOKSHannah ASHTONWillunga
1857 13/119Benjamin BROOKSYankalilla Thomas BROOKSHannah ASHTON
South Australian Register 1 May 1863 BROOKS. —On the 20th March, at Myponga, Hannah Brooks, wife of Thomas Brooks, farmer, aged 47 years, after a long and painful illness. She was very much respected, and her end was peace.
South Australian Advertiser 5 Mar 1879 McGAY—BROOKS.—On the 20th of February, at the Baptist Chapel, Stepney, by the Rev. Jacob Abbott, R. McGay, to Elizabeth Ann Brooks, third daughter of Mr. Thomas Brooks, late of Myponga.
South Australian Register 22 Apr 1873 HOW— BROOKS.-On the 9th April, at St. Stephen's Church, Willunga, by licence, by the Rev. E. K. Miller, Mr. Henry William How, to Miss Fanny Brooks, both of Aldinga.
Is this your family...can you add anything to this please? There are probably more births to find 1844 - 1853.