fibonaccifreak welcome to FlyerTalk and to the QR forum.
Because it was a zero priced ticket you will not earn any Qmiles or Qpoints.
See
http://www.qatarairways.com/us/en/of...sure-hunt.page which says 'A golden ticket is a single, zero-fare ticket to a specific destination, valid for travel between 11 January and 15 December 2017. Only taxes and surcharges apply.'