Kate Middleton heads back to official duty in royal style (PHOTOS)

Oct 21, 2014 at 10:37 a.m. ET

She's back! The Duchess of Cambridge is obviously feeling a little better because she was back on duty on Tuesday morning to welcome — along with her husband Prince William — the president of Singapore, Tony Tan Keng Yam, and his wife, Mary, to the United Kingdom.

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The Duchess of Cambridge looked beautiful in a gray coat dress by designer Alexander McQueen, which she paired with a gray fascinator by Jane Taylor. Kate and Prince William met Tan and his wife at the Royal Garden Hotel, just a few yards from their home in Kensington Palace, Us Weekly reports.

"I've been looking forward to getting out of the house," the duchess joked with the Singaporean president, adding, "It's a bit colder than when we last met," the publication reported.

The royal couple and their guests then traveled in style in a beautiful horse-drawn carriage as they made their way to the Horse Guards Parade, where they received a ceremonial welcome from the queen and the Duke of Edinburgh.

Kate Middleton travels in carriage to Horse Guards Parade

Photo credit: WENN

Kate Middleton travels in beautiful royal carriage on official duty

Photo credit: WENN

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It was Kate's first public appearance since the announcement of her pregnancy as she has been suffering from Hyperemesis Gravidarum, a serious form of morning sickness. However, this morning she looked radiant and in good health, and was happy to smile and wave to her well-wishers, many of whom were eager to see if she was sporting a teeny baby bump (it's barely visible).

The royals and their guests then continued to Buckingham Palace, where Prince William will remain for lunch, but the three-months pregnant duchess will not. Although, Kate is expected to make her second official appearance later today when she attends the Wildlife Photographer of the Year 2014 Awards Ceremony at the Natural History Museum.

The royal couple will welcome their second baby in April 2015.

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