I do find that there’s a slight tendency on the London threads for people to recommend slightly more offbeat things that are great to entertain local children during the long summer hols. I personally love Museum of Childhood, the Greenwich museums and Princess Diana playground for but actually if your spending your first 48 hours in London at the age of 9 then I’d keep it really basic and hit all the tourist cliches.
Trafalgar Square, Houses of Parliament, Changing of the Guards at Buck House, Eye/Shard/Skygarden/Monument/Tower Bridge walkway for a view, Globe, Belfast, Golden Hinde, St Paul’s (walk past the last four, not visit unless they’re her favourite things), Clipper along the Thames, Wobbly Bridge, Tower of London, See Tower Bridge opening up if poss.
And then reserve half a day for something that she’d be particularly interested in: whether that’s theatre, ballet, Lego, dinosaurs, Harry Potter, science, dead bodies, zombies, fashion, ice cream ......