Ursula's wonderful site gives a hint why the Queen decided to wear the brooch:
"It was made in October 1856 by R & S Garrard, who remodeled an existing piece of jewellery and added the stones that had been presented to the Queen by the Sultan of Turkey, Abdul Mejid I in May that year. The ratification of the Treaty of Paris ending the Crimean War occurred on April 27th between the Queen, the Emperor of Austria, the Emperor of the French, the King of Prussia, the Emperor of Russia, the King of Sardinia and the Sultan of Turkey! Perhaps it was a present for her instead of an order".
So maybe not an ideal choice for this particular gown and the rest of her choice of jewels but a great idea to honour the British-Turkish relations!