Ok Goody, even though I don't fly for the one and only airline in the Middle East, since your salary is what we lowly ATC'ers get, I may be actually qualified to respond. Of course I am sure Sandigger feels I shouldn't even be here but anyway...
Do you get any allowances on top of that, eg. Education, Accommodation, travel, utilities???
If you want to start sending the boy to school in a couple of years you will need that paid for by the employer, as otherwise it will take a big chunk out of your 15,000 AED. Also accommodation will take a huge chunk out of 15,000 AED a month.
That said if you do get the above mentioned allowances, then yes you can live very well here, and save a lot for your future wherever you choose to spend it. The exchange rate right now is bad, and there are no guarantees it will get better, and that has to also be taken into account.
As far as lifestyle goes, if you have small/no accommodation allowance, and you can only afford a small flat, I would recommend getting a membership at a club where the wife and child can sit by the pool/ on the beach and enjoy the weather. Also most of the shopping centres have play centres for the little ones, so when the weather gets hot, thats the place to spend time to keep your son happy.
I know I will get shouted down by the knockers here, but as a few guys have said before, I am just trying to give some honest advice to someone asking for it. cheers.