I contacted the Qatari consulate in Dubai and also asked a friend to go to the Ministry of Interior in Doha, Qatar. They all give the same answer --since I was only on a tourist visa which was sponsored by my wife (who worked for Qatar Airways) they do not issue a police clearance certificate unless and until I resided in the country on a residence visa. Even the CIC link here states that I need a residence visa: http://www.cic.gc.ca/english/information/security/police-cert/mid-east/qatar.asp
See point: If you live outside Qatar/ Required documents:/ a copy of your old or expired residence visa in Qatar
The people at the Qatar Consulate told me that all authorities know this procedure and that CIC should know it too. They said that I could share their name/number with CIC who could check for themselves the authenticity of my statement. Of course I doubt anyone from CIC would do that so I guess the only way for me is to convince CIC myself. Perhaps, I will scan my visa/entry/exit stamps to make them understand.
Any views?