Thank you very much, PJ Kiser, for this great picture!
Princess Anne wore this brooch at least once, in July 1980, for this official group portrait of the Queen Mother with her grandchildren, on the occasion of the Queen Mother's forthcoming 80th birthday:
Mark Phillips, Princess Anne's first husband, served in the Queen's Dragoon Guards from 1969 to 1978.
According to Wikipedia ( http://en.wikipedia.org/wiki/1st_The_Queen%27s_Dragoon_Guards ), "in 1896 Emperor Franz Joseph of Austria was appointed Colonel-in-Chief of the 1st King’s Dragoon Guards and allowed the regiment to wear the Austrian imperial coat of arms, which is still used as the regiment's cap badge today. Also the regiment adopted an Austrian military march, Radetzky March, as quick march".