I've spent layovers in London in that time frame on several occasions, and given the time of year and the age of your daughter, I'd suggest Hyde Park and some of the shopping district to the east of the park. This recommendation is weather dependent, but if it's a nice day, the park has plenty of areas, including the Hyde Park Winter Wonderland, that should be appealing to a 9-year-old, and the shopping areas in and around Oxford Street, including stores like John Lewis, Harvey Nichols, and Marks & Spencer, should be beautifully decorated. Plus that area is full of eating places of various types that should appeal to you and your daughter.