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FYI, there are reports that production of the iPad Mini has already started.
I don’t think a specific date can be identified by anyone outside of Cupertino, and perhaps not even there. I feel pretty confident saying that your idea for a Christmas present will work out though, I simply cannot imagine Apple would miss the holiday buying season unless something went really wrong. Keep in mind, there are still nearly 2 months until Black Friday, which is a date on which most companies want to make sure their new consumer products are available.
TL;DR - November, most likely.