Be wary, my friend couldn't do the fast track, they said it was unavailable at the moment so she is trudging off somewhere next Sat (she flies the following Weds) to get emergency passports. As I said though, hopefully Sept will be less busy. Good luck anyways.
When I flew back from Boston a couple of years ago there was a lady next to me with a three week old baby, she was travelling on her own, into Heathrow then on again to Aberdeen, the cabin crew were really helpful and I got plenty of cuddles with the baby whilst she went to the loo, sorted bottles etc.