"I'm in love with a working girl" was a song by a band called Members, also from the 1980s.
Irving Lewis Allen's City in Slang (1993) states: "The expression working girl was first used during the Civil War, in part to make a new social category of the increasing numbers of women in the industrial and commercial forces." (...) Early in this century she became the comic heroine of the popular song, 'Heaven Will Protect the Working Girl' (pronounced WOIKing goil), words by Edgar Smith. In the lyric a village mother says to her city-bound daughter, 'When you are in the city's giddy whirl,/ From temptations, crimes and follies,/ Villains, taxicabs and trolleys, Oh!/ Heaven will protect the working girl.' Our working girl rejected the villains's offer of a demitasse, which might have led to heaven knows what. In the marketplace of the city, the reputation of even virtuous girls was always being questioned, which our working girl protested in Edgar Smith's song lyric of 1900, 'I'm a Respectable Working Girl.' Working girl did not become a tongue-in-cheek euphemism for a prostitute until the 1960s and is another compliment that vice paid to virtue."
There is a "working girl" citation in the New York Times of July 24, 1858, but it is correct that the Civil War popularized the term and status.
Most of the "working girl" prostitution cites date from about 1966-67.