Agree that there's not a ton. The new Islamic art musem was nice, but a bit underwhelming -- was expecting more on the inside. I suppose they built the museum as big and nicely as they did in anticipation of continuing to build the collection. I'd definitely see it if going there, but maybe not make a special trip just for it.
I might have been given wrong information, but I visited Oman after Qatar and was told the free entry only worked if you went straight there, not via other countries. No idea if that's true or not.