Ok so I've tried my above mentioned receipe and found the coffee to have a bitter after taste. The "latest" receipe involves placing bit of rainbow milk and saffron threads (or saffron colour) in a kettle and adding water (usually already hot from the kettle) until it boils. then placing 1 1/2 kahwa cups of kahwa and letting it boil for 5 minutes. Once the kahwa settles (a couple of minutes) this is then pour into a thermos that has 2 teaspoons of cardamom in it.
The taste in great!! No bitter after taste - apparently that was happening because I was boiling the kahwa for too long!

About the coffee mate / rainbow milk issue. I don't think all the qatari's add it to the kahwa - but it results in lightening the colour of the kahwa which is nice.