I think the LTE iPad mini will come out as soon as Sprint rolls out its LTE plans in mid-November. According to this from Sprint, the date is November 11, 2012.
So far the WiFi + Cellular models are still in 'pre order' since they start shipping mid November. What we were told was that they start becoming available 2 weeks after the WiFi started selling in stores, so 2 weeks from Nov 2nd if that helps?