If the weather isn’t too horrible, boat trip down the river to Greenwich (lots of nice shops and restaurants there). Otherwise Windsor Castle and Eton - easy to get to from LHR and again no shortage of shops plus lots of 9yo friendly restaurants.

Bear in mind that central London (and especially public transport) will be absolutely rammed with Christmas shoppers, people partying, tourists etc and may be a bit full on with a 9yo. As you’re probably aware, Christmas and the run up to it is a big thing in the UK and places will be very busy. From that perspective, Windsor might well be a better bet (assuming the Castle is open).