mid-15c., "cry of dissatisfaction or contempt," from hoot (v.). Meaning "a laugh, something funny" is first recorded 1942. Slang sense of "smallest amount or particle" (the hoot you don't give when you don't care) is from 1891.
"A dod blasted ole fool!" answered the captain, who, till now, had been merely an amused on-looker. "Ye know all this rumpus wont do nobuddy a hoot o' good—not a hoot." ["Along Traverse Shores," Traverse City, Michigan, 1891]
Hooter in the same sense is from 1839.
HOOTER. Probably a corruption of iota. Common in New York in such phrases as "I don't care a hooter for him." "This note ain't worth a hooter." [John Russell Bartlett, "Dictionary of Americanisms," 1877]