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It's a tricky one this, but can you clarify a few things
1) Are you travelling after 1 May 2018? The minimum age for solo travel will rise on that date for new bookings, from 12 to 14 years old.
2) Is this on one reservation from LAX to CPH for you? And another reservation LAX to CPH for your daughter?
3) How long is your connection as booked?
4) Have there been any changes to flight times since you initially booked, so comparing the first email you got from BA to the current timetable.
Having said that, so long as your daughter is reasonably confident then she is safer airside in LHR T5 than almost anywhere in the USA. Some 12 year olds are weekly commuters.