Having taught in Qatar myself for a number of years I still firmly believe you should choose a school which will reflect what is the easiest curriculum to follow wherever you go in the world.
The other point to consider is where you think your child will fit in easily, be able to make good friendships and socially will be accepted by their peers.
I know this is a harsh point to make but children can at times be very cruel to each other still in this world of multicultralism, so I think you have to consider where your child will feel Happy!
If you are a native English speaker I firmly suggest that your child goes to a school where other Native English speakers attend. We all know there are very different styles and interpretations of the English language, Grammar isssues, spelling issues etc.
You will see and hear the evidence of this when you arrive.
For what it is worth, myself being a native English speaker, if I had children I personally would try to get my child into DESS, Doha College Primary or Park House. If you are from America, then the American School of Doha.
I personally really would not consider any other school here for a native English speaker.