The cocktail has a long, storied, and disputed history which GumboPages.com has in detail. Essentially, it is accepted to be created by Antoine Amedee Peychaud in the early 1800's when he mixed it with his bitters. Originally, it was made with cognac, but somewhere around 1870 Thomas Handy took over the Sazerac House and changed the base to rye whiskey and that is how the cocktail is made to this day.
This fizz came to light in the late 1800's thanks to Henry C. Ramos at Meyer's Restaurant in New Orleans. To add to the story and show just how tempting this cocktail is, there is a story about Huey P. Long (Governor of Louisiana, 1928-1932) bringing a New Orleans bartender to New York to train bartenders there so he could have a proper Ramos Fizz whenever he was in the city.
This very fruity, very rummy cocktail was a sort of fluke which I'm sure Pat O'Brien didn't think would last, certainly not this long. It was in the 1940's that O'Brien found too much rum in his bar and decided to create this drink to relinquish the majority of the supply in order to buy more the popular whiskies of the day. Well, as we can now tell, his cocktail was a hit despite his motives and has since become the ultimate party cocktail of the city and led to many hangover pains.
The place to get a Vieux Carre in New Orleans is the Carousel Bar in the Hotel Monteleone. Not only is this hotel the main site for the annual Tales of the Cocktail, but it is the birthplace of this classic cocktail although it is not as old as one may think. It wasn't until the 1930's that Walter Bergeron first mixed this libation, appropriately giving it the French name "old square," which refers to the French Quarter the hotel is nestled in.