Absolutley loads of pre-school care, but it tends to sit seperately from the schools.
There's another topic with all the school names, but basically there are dozens of nurseries in Jumeirah and Bur Dubai, plus some in the Greens area near Emirates Mall.
The only issue is how long you need it for each day. A lot of nurseries will only open 8am-1pm or 8am-3pm or something daft, basically designed around non-working mums who want a bit of a break and a structured learning area. Latest I've seen shuts at 5:30pm.
Get your name down early as the waiting lists can be long. I heard of a British Orchard nursery opening in Bur Dubai this week, one option although you have time on your side.
If that doesn't suit and you only need it for a few months, I'd consider getting a live in maid/ childcare for that period. It's not perfect but as it's only for a few months it's not going to ruin your kid's life. I believe the cost is really cheap, say around 2000Dhs a month (close to 300 quid) and they'll clean and look after your child. You have to provide a room and food for the period as well. If you're here before the family there will be loads of opportunity to find someone, the local supermarkets are full of adverts and people at your work will be able to recommend too.
Finally (phew!), there are professional child care companies and also child carers who won't live in with you but are a bit more expensive and charge by the hour. They'd cost say 20Dhs-25Dhs an hour (GBP3-3.50). Again, easy to come by once you're here.
Finally, school registrations for the autumn are under way already so put that on your list as an early thing to do when you arrive.