I can't find them in the 1900 Census, but various Little Rock city directories (from 1883-84, 1887, 1890, 1893-94, 1895-96, 1897-98, and 1899) list Noah Hamlet, a brick mason/contractor.
However, in the 1900 Census in Little Rock - Big Rock Township, there's a Fred Hamlet, born Nov. 1880 in Arkansas, father b. England, mother b. Ireland. Also living with him is Noah Hamlet, b. Sept. 1882 with same birth place & parents' birth places as Fred. They are living as boarders in the home of John Smart & family. Neither Fred nor Noah have an occupation listed. There is a WWI Draft Registration Card for Noah Hamlet, living in Little Rock, b. 21 Sep 1883, native born. It says he was an inmate of Pulaski Co. Hospital, was "mentally defective", and had the loss of his left limb. It says he has no relatives.
On the Arkansas death index from 1914-1950, there is a Noah Hamlet who died 7 Feb. 1919 in Pulaski Co., but there's no information about his age, place of birth, etc.