Quirrell takes a year off from Hogwarts for some first hand experience fighting the Dark Arts. He will be gone from September 1990 through June of 1991. While in Albania, he encounters Voldemort and brings him back.
There is no specific canon reference to indicate which year Quirrell took off from teaching. However, Dumbledore specifically says in HBP20, "we have never been able to keep a Defence Against the Dark Arts teacher for longer than a year since I refused the post to Lord Voldemort." Therefore, since we know Quirrell taught in 1991-1992, he could not have taught from 1990-1991. This, then, was almost certainly his year off.
However, Hagrid speaks of Quirrell's nervousness as the result of his year off, and if that year off had been the 1990-1991 school year (the one immediately before Harry comes to Hogwarts), Hagrid seemingly wouldn't have known about Quirrell's altered behavior:
"Poor bloke. Brilliant mind. He was fine while he was studyin' outta books but then he took a year off ter get some firsthand experience...They say he met vampires in the Black Forest, and there was a nasty bit o' trouble with a hag--never been the same since. Scared of the students, scared of his own subject now..." (PS5)
This doesn't seem to align, but it is possible that Hagrid is just talking about the month or two since Quirrell has returned from Albania. And if we take Dumbledore at his word, nothing else really makes sense.
Rowling writes about Quirrell's Grand Tour and his motivation for trying to find Voldemort in Albania. She doesn't clear up the mystery of when he was gone from Hogwarts (Pm1.17.1).