There is another one on Al Saad, it takes kids over a year old. I had just posted this exact question this morning :)

I have been recommended this nursery called Al-Abrar twice, they have 2 branches: 4867048 Al-Lukta ( near immigration )and one on 4365548 Al-Sadd. The fees are around QR 500 monthly and they are open from 6:30 am till 2:00 pm