The only costumes available retail here are the 'cheap and nasty' touristy sets that are sold down in the souq, they're made in India and quite honestly no self respecting dancer would be seen dead in one
Fabric here is a good buy though it'd be difficult for your friend to buy on your behalf. Skirts etc can be made here really cheaply. You can take a photo of a dress you like or a pic from a magazine to a good tailor in Satwa (which fortunately for me is near where I live) and they'll make something almost as good as the real thing. Its amazing.
For coverups, your friend could go upmarket to the shops in BurJuman where they sell the black abayas and also the colourful inside dresses that you could use as a coverup or go to any of the local shops even Carrefour where I bought a gorgeous gold Moroccan style gown for 75AED.