[GKnH]

My daughter is older than yours but the advice we had was wear regular holiday outfits in resort and cover shoulders and knees when out and about. However, we did a walking tour in Old Dubai and me and DD followed those rules but another lady on the tour had above the knee shorts and a strappy vest top and had no problems.
I think if you were visiting a mosque you'd need to cover up (to be respectful) but an 11 year old would be fine anywhere else in Dubai in normal child clothing.

I know there are some real Dubai experts on here who will be able to advise you also.