I'm not in Dubai now, but was for 8 years.
At the end of Aug it will still be VERY hot - over 100F every day. Essentially, you will wear summer clothes the whole year round. Best to go for cotton and other natural fabrics that breathe. I wore skirts most of the time as I found them much cooler than trousers, but sometime wore crops/linen or looseish trousers. Wear cotton undies too!. I can't remember ever wearing a pair of closed in shoes the whole time I was there and I now have a marvellous cupboard full of sandals that I hardly ever get to wear.
In the winter when the temperature plummets to 19 or 20c(!), you may need a light cardi and also the aircon can be fierce especially in the cinema. You will also need warmer clothes for return trips home, but you will not need a coat in Dubai.
For your little one, just lightweight, loose, cotton things. For DH it will depend on his company "uniform" my DH just wore trousers and short sleeve formal shirts. All the offices are air conditioned and so are a steady temperature in the low-mid 20's.
Don't worry too much though as you can buy what you need in Dubai. There is MnS, Debenhams, Next, Gap, H & M, Zara, Mothercare, Boots as well as lots of other brands from around the world. One thing Dubai is not short of is shops!
When you arrive you will feel like you are in an oven but it's amazing how you get used to it. If you don't already have them, you will need lightweight duvets if a sheet isn't enough but again there is Ikea for all that kind of thing.
Good luck with the move. for all its faults I loved Dubai.