The earliest match I could find for this call and response (in its short form) is from Albert Smith, The Fortunes of the Scattergood Family, serialized in in Bentley's Miscellany, volume 15 (1844):
They [four larger schoolboys at Merchant Tailors] lifted the box on to the table, and then made Frederick who was beginning to cry very piteously, open the lock. The first thing they saw was the accordion, which Mr. Bodle had given him, and which Gogsley directly seized on, holding up at arms' length, and shouting out,
"Ego!" cried the other three all at once.
"Yours, Plunkett," he exclaimed, handing it over to a genteel-looking youth, in broad lay-down collars, who directly commenced a very rapid fantasia upon it, introducing no particular air, which terminated in putting several of the notes entire hors de combat.
And likewise from "The Little Handful of Thorns," in The Sunday at Home: A Family Magazine for Sabbath (1875):
A summer day ; earnestly hot. Never mind, it is necessary for the rector to go to Chee-combe (a little hamlet in his parish) to see old Thomas Warne. "Who will go with me? Quis?" "Ego!" shouts the youngest girl, an exceeding fatling of three years old (precociously imitating her brother's Latin, to his delight). " No, not you, my pet ; the stout, sturdy legs are not equal to a walk over these hills ; not yet, at least. But Siward and Elgiva, they, if they like may come with father."
Eric Partridge, A Dictionary of Slang and Unconventional English, second edition (1938) has this entry for the expression:
quis? Who wants some? : Public-Schoolboys' : mid-C. 19–20. The answer is ego! [W.E.] Collinson [Contemporary English (1927)]. Direct ex Latin.
It thus appears that the schoolboy call and response of "Quis?" "Ego!" antedates by at least 55 years the earliest OED citation noted in Barrie England's answer. Like Barrie England, I could not find any trace of "Quis?" "Ego de to my liking."