Brick Red Coat and Hat Trimmed with Velvet Roses

Brick red coat with quilted collar, cuffs and patch pockets, with a satin-covered toque-style hat with a small brim, trimmed with red velvet roses.
The Queen chose this look for the graduation of her grandson, Prince William, as a commissioned officer in the British Army during the Sovereign's Parade at the Royal Military Academy Sandhurst on 15 December 2006. She complemented the red fabric with the ruby and diamond Australian Hibiscus brooch:

The Queen wore this outfit again on 16 April 2010 to attend the Newbury horse races. No brooch was used:

On 30 November 2011, the Queen selected this look again for a visit to the Musuem of Liverpool (during which HM met Yoko Ono), accessorizing with her Grima ruby and Yellow gold brooch:

Unfortunately, I have no reliable info on the whereabouts of this coatless appearance, complete with Red Flower Posy brooch: