Perry, the proof you seek is at the Georgia Department of Archives and History in Garrett's probate file. It names not only Leona Adelaide, but also the other surviving children, particularly those underage and entitled to special orphan support as part of the probate proceedings. See also 1860 census.
Gerrit Yzaacszen "Garrett" Hallenbeck married twice. By his first wife, Maria Matilda LaHatt (m 24 Oct 1818 in NY, she d 1826 in NY), he had four children, of whom only Sarah Leonora Hallenbeck Dimon remained living at time of probate. His second wife was Martha Ann Trotter (m 22 Nov 1838 in Russell Co AL, she d 12 Apr 1874 Columbus), who served as executor and guardian for the minor children. At her demise, executorship was assumed, if memory serves, by William H H Blankenship, husband of the oldest daughter, Martha Ann Josephine. According to cemetery records, Martha is buried next to Garrett, probably beneath the unmarked pile of crumbling bricks. Several unmarried children are in the same lot, and possibly both Theresa Parr and Sophine Keith.
My husband descends from Sophia Leonora, which makes us cousins. See my extensive tree at RootsWeb.