I am confused by Quirrell's behavior in attempting to kill the auror, so I assume that there is something that I don't know or understand about Quirrell's motives.

What I don't see yet is that Quirrell was relying on the dual to occur, only that it was a possibility that he accounted for.

You're right, that's all we can know for sure from the story so far. My theory is purely speculative, a guess at Quirrell's true motives. It springs more from earlier chapters than from this one: I think it was really suspicious of Quirrell to go to all that trouble to bring Dementors into Hogwarts, and I'm inclined to believe that Hermione got true information from her encounter with the Dementor (namely, that Quirrell wanted Harry drained). Given that background, it seems more than a little suspicious that Quirrell has brought Harry into the same danger all over again, which is why I'm so quick to believe that stripping Harry of his Patronus was part of the plan. But I definitely don't think I have all the details worked out.

Assuming that this was part of the Plan, in some sense, then it comes across to me as a test.

But in that case isn't he risking a lot for very little reward?