It says: "Harry does not see him die in the book, although he does in the film. This error will cause some problems later in the story, since Harry should be seeing the thestrals already in his third year if he had seen Quirrel die."
So according to the book, he didn't see Quirrel die, but he saw Cedric die at the end of book 4 and sees the thestrals at the beginning of #5.
I so wish the movies would stick to the facts!! It gets too confusing!!
I just had a "Duh" moment about year 1. The first years didn't ride in the coaches. They took boats.