Hi,
i visit Erbil last month, i stay in Enkawa too, nice place and safety too, for the nursery i found one in Enkawa and i thing its the only one there Managed by nuns, its not international but it can take care of you kind.
i still didn't deiced if i will move with my kind there but i had take a look in the aria there and visit The International School of Choueifat,and most people there recommended it for the Constituent educational stage, maybe i will move there in August, i don't know yet.