Granola, IMO the suggested play area would be unsuitable for your 1 yo, and my 3yo got knocked around a bit by some older children in there. I usually take her to Hamley's Toy Store to have a play with the display toys or at ELC. She likes the small play area at the Organic Cafe, which is a great opportunity for us both to grab a drink (not now though).
If you could go to Mirdif CC instead then the play area inside Magic Planet is fantastic, or Little Explorers:)
Thanks ladies. I will go check them out without promising anything to the kids just in case!
If it doesn't work, there's always the toy store to run around in, which I'm sure Hamley's appreciates...
There is a lovely play area in the food court (upstairs one opposite the Underwater Zoo exit) that's really good for the age groups you're looking for :)
There is a kiddie area upstairs in kidzania I found as I took my eldest there not sure if u can just take the little ones in there though ? Apart from that there's nothing ....