It was a Qatar airways PNR. DOH > CPH on Qatar, CPH > KEF on SAS.

What has qatar airways got to do with providing compensation for the entire journey? They told us (when called to find out how to file as their online link goes no where) to talk to SAS - its their problem.
SAS segment is the only relevant thing here and it's basically that the SAS journey (with an SAS flight number) is a separate segment itself - Qatar airways are treating it as such.