With regard to the geographical and chronological origin of the term "Pixie Cut," I found this instance from "Fashion Show Features New Ideas and Styles," in the Santa Monica [California] College Corsair (April 25, 1951):
Are you looking for fresh ideas for smart styles? Some simple and economical clothes you can wear with a flair that mark the smart dresser and campus coed?
Then you'll want to see the City College Fashion Review at 11:00 next Tuesday in the City College auditorium.
You'll want to see the Pixie Cut, Fascination, Blue Nocturne, Dream Bait, and Sugar and Spice, just a few of many of the latest hair stylings which will be shown by 24 models. All of these designs are by students from the cosmetology class under the direction of Beulah Grace, of the Technical School.
Santa Monica is on the edge of Los Angeles and therefore not an unlikely place to encounter early notices about emerging style trends.
The first photo of a Pixie Cut that I've been able to find appears in an advertisement in the [Suffern, New York] Ramapo Valley Independent (May 15, 1952), and I must say that it doesn't look much like the modern-day notion of a Pixie Cut. The ad reads as follows, but you'll have to click the link to see the photo:
“The Pixie Cut"
Our Hair Style of the Month
GENE'S Barber and Beauty Shop
68 Lafayette Ave., Suf. 5-0210
An item in Earl Wilson, "It Happened Last Night," in the Indianapolis Times (February 22, 1952) credits John Fonda with "creating" a Pixie Cut being worn about town by Veronica Lake—but the accompanying photo of Ms. Lake is so shadowy that it's impossible to tell whether she is sporting the new coiffure in the picture or not. Wilson was a nationally syndicated columnist based in New York City.
It seems to me that the question "What is the [etymological] origin of the term 'pixie cut'?" is no more answerable than the equally perplexing questions "What is the [etymological] origin of 'Blue Nocturne' as a hair style?" "What is the [etymological] origin of 'Sugar and Spice' as a hair style?" and "What is the [etymological] origin of 'Dream Bait' as a hair style?"
The most likely origin of "Pixie Cut" is simple fortuity: someone like Beulah Grace (although probably not her) made up a new hair style and sought to increase its appeal by giving it a catchy name—or a name with cachet. I think it is highly unlikely that most people in 1950 shared a clear idea of what a typical pixie's haircut should look like and then a stylist tried to replicate that look. If my surmise is correct, we search in vain for an etymological answer, and every inquiry merely multiplies the questions: "Why 'Blue Nocturne' instead of "Blue Steel'?" "Why 'Fascination' instead of 'El Tigre'?" "Why 'Pixie' instead of 'Dixie'?"
In hindsight, it seems clear that people thought the name sounded cute and the haircut looked cute—and that potent combination helped "Pixie Cut" defy the odds and flourish through the decades, while "Dream Bait" and "Blue Nocturne" fell by the wayside.