The best two schools for primary school are DESS and ASD. Doha College is not far behind. Both DESS and Doha College follow the English national curriculum, and DESS preferences students with British passports. However, these are all oversubscribed.

Qatar Academy is well-founded and has excellent facilities. It is, however, overwhelmingly Arab (mostly Qatari) if that is a concern for you.

Sherborn is new but has a good reputation. I would group it in term of overall quality with Compass and Park House (although each have their individual strengths and weaknesses).

Based on what has been posted on QL and what has been stated by parents, the Newton system is substantially below this group. Others may disagree; but just do a search on QL of this and any of the schools you are considering.