Londoner here! I hate Oxford street with a passion, to be honest it is mostly the same chain stores which most high streets have and is ram packed full of tourists and sadly pick pockets.. I would take your DD down Bond Street for a gawp at the posh shops, then go and have fun at Camden, Carnaby Street or Covent Garden. I like Marylebone High Street too. If the weather turns then go to Stratford to the Westfield Mall , seems to entertain most of East Londons teens!
For a quick look at the sights since you haven't got much time then either take one of the hop on hop off buses or there is a normal bus which covers a lot of the same ground.
I like the London Eye and on a good day gives you a unique view, but Sky Garden is free (you MUST book and bring ID) and gives you the best view of the shard.
You won't get to see everything in two days, so do your research about what she really wants to see, eg some places like Madame Tussaud's are very busy,and have long queues so you could waste most of a morning, though I think you can pay for pricey priority tickets.
On my to do list I would want
A boat trip. You will see lots of famous buildings / sights from the river.
A walk along southbank (preferably at the weekend)
A visit to one of Londons fabulous open spaces, maybe combined with a visit to say Kensington Palace or the Serpentine Gallery.
A shopping /window shopping excursion.
Since your daughter is 14 you would be well advised to apply now for a zip card (see the Transport for London site) to deal with transport costs.
Worth downloading TFL onto your phone for what's on ,travel advice and updates.