More interesting is the origins of that phrase to designate prostitution.

Fortunately, I found an article in worldhistories.net, that shows the first documented time of this phrase. The person who coined the phrase was none other than Ruyard Kipling ("The Jungle Book"):

Lalun is a member of the most ancient profession in the world. Lilith was her very-great-grandmamma, and that was before the days of Eve as every one knows. In the West, people say rude things about Lalun’s profession, and write lectures about it, and distribute the lectures to young persons in order that Morality may be preserved. In the East where the profession is hereditary, descending from mother to daughter, nobody writes lectures or takes any notice, and that is a distinct proof of the inability of the East to manage its own affairs.

- On the City Wall, in In Black and White (Allahabad: A. H. Wheeler & Co., 1889), page 78

If you want to know about actual prostitution, we should go far back to ancient Mesopotamian texts.

According to "The Epic of Gilgamesh" (the most ancient epic in the world), the gods created a savage man, Enkidu, who lived in harmony with the animals in the woods. Gilgamesh wants to tame Enkidu, and is told to bring a "harimtu" (a "sacred prostitute") to him.

and he [Enkidu] possessed her ripeness. She was not bashful as she welcomed his ardor. She laid aside her cloth and he rested upon her. She treated him, the savage, to a woman’s task, as his love was drawn unto her.”

Later, as he regrets joining civilization, Enkidu curses the harimtu:

“I will curse you with a great curse… you shall not build a house for your debauch you shall not enter the tavern of girls…. May waste places be your couch, May the shadow of the town-wall be your stand May thorn and bramble skin your feet May drunkard and toper (ed note: someone who drinks alcohol to excess) alike slap your cheek.”

Researcher Gerda Lerner, in her article "The Origin of Prostitution in Ancient Mesoportamia" (Signs, 1986, pp. 245-6), says:

The nature of this curse tells us that the harimtu who mated with Enkidu lived an easier and better life than the harlot who has her stand at the town wall and is abused by her drunken customers.

This would confirm the distinction we made earlier between the women engaged in various forms of sacral sexual service and commercial prostitutes. Such a distinction was more likely to have existed in the earlier period than later.”

So yes, there were prostitutes in ancient Mesopotamia, the cradle of civilization.

EDIT: typo