I can not imagine that the Queen of the Netherlands would wear fake when she has such an enormous amount of jewels and bijoux at her disposal. I have also the idea that the stones in the brooch are not exactly the same in shape or size, which is in my opinion a hint that it is about real stones.
I like the combination with the white centre stone (pearl?) and Beatrix, as detailed as always, wears a matching amethyst hatpin.
Eye for detail: the inside lining of the cape matched the purple ensemble the Queen wore.