Granted with no kids of my own, I don't have too much insight into this, but I do know my bookshops
And a lot of this information comes as tips from friends in Egypt who would like their kids to learn to read Arabic just to make the transition easier.
1. The best place/time to find them is at the Cairo International Book fair because publishers from other Arab countries that don't have stores/distribution in Egypt sell their stuff there.
2. Dar el Shorouk publishes Arabic books for children and sells them at their outlets in the Four Seasons First Mall, City Stars Mall (the extension), and Korba. Their kids section in Arabic is one of the strongest around town.
Shorouk publishes series of books from Alam Simsim (sesame street), the Mister books (Mister Happy etc), Miffy and more. There are Barney story books and other famous characters as well. Someone mentioned that the new series by Shorouk are in Egyptian Arabic, but printed in China. Books start from about 10LE each.
3. The lovely ladies at The Bookspot, don't always carry Arabic books, but they do special order them so if you have something specific in mind they can always get it for you.
4. Diwan carries a few too, but its a limited selection.
5. Carre four & Hyper One have some Arabic Childrens books in their Books & Magazine sections.
Surprisingly, a lot of my friends have found better range and quality of Arabic books for children outside Egypt.