Hi
You can also check INTERNATIONAL SCHOOL OF CHOUEIFAT. I registered my 6 yrs old boy and 4 yrs girl in this school, it is one of the best regional schools in the Middle East.
They have 2 branches, one inside erbil and another on the massif road. Also they have branch in Sulaymaniyah. The good thing is that they run the same curriculum in all countries in the middle-east (UAE, Qatar, Saudi, Jordan, Lebanon, Egypt...). So if u plan to relocate to another country in the future, you should consider this option.
Check the website
iscdreamcity-sabis.net
iscerbil-sabis.net