@hk88 [long]
I've lived in HK for 12 years and both my kids are at the British international school (Kellett). The other schools that teach the English curriculum are Harrow and Nord Anglia. There are loads of other English medium schools but they usually teach the PYP (IB) curriculum or a country specific curriculum (eg Australian School). Be aware that cut offs for years vary, so if your daughter was born between September and December she'd be in a higher year in some schools (e.g. ESF) than in the UK system. Kellett usually has a long waitlist but is culturally still quite British (very "happy" school - great pastoral care and holistic focus, as inclusive as it gets). Harrow is an international school in name only (90%+ local kids). Nord Anglia has a good reputation and is somewhere between the two on demographics. Why am I telling you this and probably sounding slightly racist? Because ultimately, whatever curriculum they teach, if there's a heavy majority of local students, the culture will be local (lots of homework, heavy academic focus, minimal playdates because they all have tutoring after school). Just be aware of that because that approach wouldn't have worked for my kids. Caveat: I have friends with kids in the local (government) system and it works for them, so depends on your kid. Issue is, they built a tonne of new franchise international schools (Malvern, Shrewsbury etc) and now cant fill them as not enough expats.
Anyway, to back up a bit, I would firstly do your research on whether this is a good move. You probably know the recent history - we had major political protests here in H2 2019 which has had fallout. There is no doubt in most people's minds that HK is now undergoing an accelerated process of political, legal and economic reintegration into China, and in particular, into the Greater Bay Area, which also comprises the Chinese cities of Guangzhou and Shenzhen. This, combined with the impact of Covid means that HK is on limited time as the truly international city that has given it its unique "vibe". It also implies far more limited opportunities for non-Mandarin speakers. HK is basically having one mother of an identity/ mid life crisis.
Re. exodus mentioned above, it's a bit hard to tell at the moment as there are some temporary moves but my observation is that far more people are going than coming - partly by choice, partly because it's harder to get a visa. Cathay downgraded a load of old (generous) contracts which means that a lot of expat pilots' families are going home as financially ruinous to stay.
My advice would be, if it makes sense financially (low taxes) or career-wise, then probably worth coming but really do your sums. There are upsides, albeit they come at a cost as it is a very very expensive city.- a kids gym class can easily be 20 quid a time. It's a great base to explore Asia if flights open up, although likely to be way more expensive/ hassle than previously- I suspect casual weekends in Thailand or Singapore wont happen for a longtime. Financially , really do the sums as 5k (50,000 HKD) is actually not a large housing budget in HK- I know that sounds ridiculous. We pay almost 70k for a 3 bed apartment in mid levels with a very old finish (the kitchen dates from the 80's). If your dd went to Nord Anglia or Kellett in Kowloon Bay then Clearwater Bay and Sai Kung would be your best bets for your budget, especially as you have a dog. That is a longer commute into Central but if you're in London now you're possibly used to that and there's a big expat contingent up there.
Best FB groups - British Mums in HK is genuinely a nice group but be aware that there's a large "HK born" contingent who would have a different perspective on the benefits of HK vs UK than maybe a shorter term expat (weird mix of "keep calm and carry on" nostalgia and a view of UK as the badlands). Avoid HK Moms. Very trolly and fighty. Just not nice or constructive.
HTH. Don't want to be doom and gloom but as you don't have to make a quick decision, worth really kicking the tyres and weighing it up. See how things pan out for us over the next 6 months at least.