Kate Middleton's first speech as Duchess

(CBS News) Kate Middleton took one of her last big steps as a new member of the royal family -- she gave her first speech as the Duchess of Cambridge at a charity event for a children's hospital.

It's been almost a year since the royal wedding of Kate Middleton and Prince William, and while her job thus far has been primarily to meet people, this was her opportunity to prove that she can publicly speak to them, too.

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So, instead of just waving, smiling and looking fabulous, she gave a few brief words at the East Anglia's Children's Hospice in the English port town of Ipswich -- without the help of her husband, Prince William, who has been away on his other job as a helicopter pilot. And while she seemed a little bit nervous, she seems to have taken very well to her role as a member of the royal family that the public very much wants to see.

After thanking the crowd for accepting her as a patron and welcoming her, she told them that the work they do is inspirational and that she is proud to be associated with it.

"The feelings you inspire -- feelings of love and of hope -- offer a chance to families to live a life they never thought could be possible," the Duchess said.

Kate has been making more and more appearances and that seems to suit the royal family -- a family that knows its public relations very well.

Prince William is due to return from his posting in the Falkland Islands this week.

To see the full report from Mark Phillips, click on the video in the player above.