Aside from the discrepancies noted below, this sounds very much like "The Choice", a 1952 short short story by Wayland Hilton-Young which was also the answer to this question. The story has been reprinted under various covers, and the full text (all 200-odd words of it) is available here.
There are two characters, the one who travels to the future, and the first-person narrator who does not:
Before Williams went into the future he bought a camera and a tape recording machine and learned shorthand. That night, when all was ready, we made coffee and put out brandy and glasses against his return.
The time traveler remembers nothing of the trip except that he chose to have his memory erased before returning to his own time:
"I can remember only one thing."
"What was that?"
"I was shown everything, and I was given the choice whether I should remember it or not after I got back."
"And you chose not to? But what an extraordinary thing to—"
"Isn't it?" he said. "One can't help wondering why."
However, the time traveler is not a girl; he is referred to by masculine pronouns. (We have no clue to the narrator's sex.) And there is no Canadian content, as far as I can tell. The story was originally published in Punch, a British magazine. If the author is the same person as this Wayland Hilton Young, 2nd Baron Kennet (1923–2009), he does not seem to be Canadian.
