We moved back from Dubai last may and had a 2 year old.
We lived in the jumeirah area and our little one went to blossom nursery which I believe has since been voted the best nursery in The Dubai awards.
A good website to look at is
www.expatwoman.com for anything and everything and
www.dubizzle.com for rental prices in the various areas. A lot of families get maids out in dubai to help out with kids but don't rely on them to be full time nannies as they're not qualified. Hope this helps a little... Let me know if you'd like any further info, am happy to help !