In the Indian Ocean? As so often happens, seemingly easy questions end up being harder than I expect. But, based on my reading of Wikipedia, the best answer is Yes. Not to be cryptic about it, it is in a body of water with a separate name, but which is usually considered to be part of the Indian Ocean.
Bikini? No.

Bay of Bengal? No.

Independent country? No.
South China Sea? No. (That's part of the Pacific.)
Al Hallaniyah? No.
One of the Maldives? No.
I'll just clarify one thing: this island is part of an archipelago by the standard definition, which is pretty broad -- that is, it is part of a group of islands. But focusing on well-known archipelagos is unlikely to be helpful. (My first reaction when I read Rosie's archipelago was that this island is not part of an archipelago, and it was only when I checked the definition of the word that I decided that it in fact is.)