First attested in 1916, the noun Brownie designates either a member of the junior branch of the Girl Scouts in the United States, for girls aged between about six and eight, or a member of the junior branch of the Guide Association in Britain, for girls aged between about seven and ten.
(According to the official website of the Guide Association, the Brownies were initially called Rosebuds.)
It is often said—for example in the Oxford English Dictionary (2nd edition, 1989)—that the name Brownie alludes to the fact that the Brownies’ uniform is brown, but it is more likely that this colour alludes to the name itself, since this name refers in reality to brownie defined as follows in A New English Dictionary (1st edition – Oxford, 1888)—as the Oxford English Dictionary was known:
A benevolent spirit or goblin, of shaggy appearance, supposed to haunt old houses, especially farmhouses, in Scotland, and sometimes to perform useful household work while the family were asleep.
Robert Stephenson Smyth Baden-Powell (1857-1941), English army officer and founder of the Boy Scouts and Girl Guides, made this reference clear in the opening lines of the chapter Brownies of Scouting for Girls: Adapted from Girl Guiding (New York, 1918):
A Brownie is a household fairy who lives under and in the trees. This is the reason that the Brownies badge is an acorn.
There are many kinds of Brownies, such as Sprites, Elves, Gnomes, Fairies, Goblins, Pixies, Imps, Nymphs, Will-o’-the-wisps.
According to several sources¹, Robert Baden-Bowell borrowed the name of the junior branch of the Girl Guides from The Brownies², by Juliana Horatia Ewing (née Gatty – 1841-85), English author of children’s stories; the little heroes of the story in question, Tommy and Johnnie, begin as lazy boggarts and become helpful brownies.
¹ Among these sources are the Victorian Women Writers Project (Indiana University) and Scotland’s Early Literature for Children Initiative (University of Edinburgh).
² published in The Brownies and Other Tales (London and Boston, 1871), illustrations by George Cruikshank (1792-1878)
Incidentally, the popular theory that the noun brownie point is from the notion that Brownies earn points for good deeds is probably erroneous.
an old Brownie-badge, representing the benevolent elf
(the letters GG are for Girl Guides, whose symbol is the Trefoil.)