It really depends on the age of your daughter. I assume she isn’t too little because of the Taylor Swift mention. If you only have one day you aren’t going to see everything, and you also don’t want to spend too much of that day moving around.
So either head East to Stratford and spend some of the the day at Westfield , she will probably love Sephora, and some at the Elizabeth park next door ( the former Olympic Park) . You could go up the Mittel Tower, you could bring your swimming stuff and swim in the amazing Olympic pool, take a ride on a canal boat or a swan, hire a bike, enjoy the park, maybe even give her the gift of real music and book a show at the ABBA Concert.
Or stay up in town, start at Trafalgar Square, walk down to The Embankment and stroll along the River to Big Ben, take in the view of the Houses of Parliament, then walk down Birdcage to Buckingham Palace, back up the Mall or through St James Park towards Trafalgar Square again . Then I would either cross the River and visit the South Bank, which is always buzzy at the weekends, or make my way to Covent Garden and enjoy some street theatre and then explore some of the shops in the market or in the streets around.. Good for chocolate. China Town and Leicester Square another option here.
Or have a Museum Day, check out what exhibitions are on at the V and A if your daughter likes fashion, theatre or jewellery , or the Natural History or Sciience Museums if that is more her style.
Or take a commuter river boat down to Greenwich, you will see lots of London on the way, Canary Wharf, Tower Bridge, OXO Tower, HMS Belfast Tate Modern,The Tower of London, Cutty Sark,St Paul’s - if you are very quick, the Millenium Bridge ( not in that order) then lots to see and do in Greenwich, museums, markets, a lovely park.
Have a great day, and next time come and enjoy London for longer, we Londoners are friendly and helpful and love people enjoying our city , as long as they stand on the right when going up or down escalators.