Unless you are willing to pay for the move (BA often offer paid upgrades at check-in, and sometimes will do paid upgrade on board) I really wouldn't recommend making the first topic of conversation at the aircraft door a hint at getting a free upgrade - I'm sure the CSD (CSM on Mixed Fleet Routes) would handle the situation professionally but there's scope for embarrassment...
This!
Asking for the CSD and then "asking for an upgrade as a single traveller" is really bad advice if you want to make a numpty of yourself. BA has a complicated algorithm that works out upgrades. Most go to passengers with status, often with the hope that they will like the upgraded cabin so much that next time they fly with BA, they'll book in the higher cabin. As a non-status passenger, chances of an upgrade are low unless you're willing to pay for one. Occasionally people get lucky because a family needs to sit together but didn't prebook or a seat is broken etc but it's increasingly rare these days. London-HK is a fairly high status route.
Also be aware that the 'best' seats are blocked for passengers with status (who can reserve these better seats for free) although these get released in the last 24 hours if they've not been booked so your daughter may get lucky (unlikely on a busy route like Lon-HK).
Someone said that HK is a big airport but that's not really true. You may have to get the transit train depending on which wing you land at but there's not a huge amount of walking in HK. Certainly nothing like the walking you do at Heathrow. HKIA is a very efficient airport. Bags come out quickly, it's all pretty seamless.
Finally, your daugher will have a better chance of empty seats around here if she books a seat near the back of the plane. Most people like to sit near the front (especially the Chinese!) but if she's not in a rush to deplane, she's more likely to get an empty seat next to her if she's at the back of the bus.
(Just to explain my comments, I live in London now but used to live and work in Hong Kong, although I always kept a base in London. I still have BA status although for Lon-HK I much prefer Emirates or Qatar).