But there's nothing in the situation that would have come as a surprise to Quirrell. If his goals were the ones he stated to Harry, then Quirrell is indeed left holding the Idiot Ball.
EDIT: By "nothing in the situation that would have come as a surprise," I mean the fact that there's a duel with an auror in Azkaban, and that Harry is present and observing. In that situation casting a Killing Curse is idiotic, if the goal is simply to keep moving with minimum fuss. Quirrell would have known that perfectly well when he was making his plan.
He could have confidently foreseen that the AK would have ruined the "perfect crime" and pissed Harry off.
He could not have confidently foreseen that Harry's Patronus would teleport in the way, block the Killing Curse, cause a magical backlash, and disappear.
[Update: and now there's a fifth discussion thread, which you should probably use in preference to this one. Later update: and a sixth -- in the discussion section, which is where these threads are living for now on. Also: tag for HP threads in the main section, and tag for HP threads in the discussion section.]
The third discussion thread is above 500 comments now, just like the others, so it's time for a new one. Predecessors: one, two, three. For anyone who's been on Mars and doesn't know what this is about: it's Eliezer's remarkable Harry Potter fanfic.
Spoiler warning and helpful suggestion (copied from those in the earlier threads):
Spoiler Warning: this thread contains unrot13'd spoilers for Harry Potter and the Methods of Rationality up to the current chapter and for the original Harry Potter series. Please continue to use rot13 for spoilers to other works of fiction, or if you have insider knowledge of future chapters of Harry Potter and the Methods of Rationality.
A suggestion: mention at the top of your comment which chapter you're commenting on, or what chapter you're up to, so that people can understand the context of your comment even after more chapters have been posted. This can also help people avoid reading spoilers for a new chapter before they realize that there is a new chapter.