"large marsupial mammal of Australia," 1770, used by Capt. Cook and botanist Joseph Banks (who first reported the species to Europeans), supposedly representing a native word from northeast Queensland, Australia, but often said to be unknown now in any native language. However, according to Australian linguist R.M.W. Dixon ("The Languages of Australia," Cambridge, 1980), the word probably is from Guugu Yimidhirr (Endeavour River-area Aborigine language) /gaNurru/ "large black kangaroo."
In 1898 the pioneer ethnologist W.E. Roth wrote a letter to the Australasian pointing out that gang-oo-roo did mean 'kangaroo' in Guugu Yimidhirr, but this newspaper correspondence went unnoticed by lexicographers. Finally the observations of Cook and Roth were confirmed when in 1972 the anthropologist John Haviland began intensive study of Guugu Yimidhirr and again recorded /gaNurru/. [Dixon]
Kangaroo court is American English, first recorded 1850 in a Southwestern context (also mustang court), from notion of proceeding by leaps.
"young kangaroo," 1839, sometimes said to be from a native Australian word joè, but more recently often said to be of unknown origin. Perhaps an extended use of Joey, the familiar form of the male proper name Joseph, for which Partridge lists many common or coarse meanings in 20c. Australian slang. Farmer and Henley ("Slang and Its Analogues") quote an 1887 article on "Australian Colloquialisms":
JOEY is a familiar name for anything young or small, and is applied indifferently to a puppy, or a kitten, or a child, while a WOOD-AND-WATER-JOEY is a hanger about hotels and a doer of odd jobs.