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Semaphore has effectively already answered the question in the comments: the 'Star of Creation' (as it is known in a Christian context) was a symbol used by Christians as well as Jews. That said, it is somewhat unusual - I couldn't find any examples of 16th century jewellery with a star based on a quick Google ...
But there is absolutely no question of any Jewish connection. All Jews were expelled from England in 1290 after period of anti-semitism, persecution and massacre. Between then and 1655 there is almost no mention of Jews in England and it would have been simply unthinkable to openly display a symbol that identified one as Jewish. Rather, the point is that Judaism was so little known or understood in early modern England that a six pointed star simply would not have been considered as inherently 'Jewish'.
There's a slightly larger image here: http://c8.alamy.com/comp/B8XF21/lady-arabella-stuart-aged-23-months-by-anon-1577-a-portrait-at-hardwick-B8XF21.jpg
For what it's worth, I don't think star contains a crucifix, but it does seem to have a vertical bar down the middle of the design.