Moving a dog to Hong Kong is not easy but not very complicated. Overall, very doable.
We moved our dog and cat from Canada to HK about a year ago. And all went well, and our dog is a happy dog now.
You can either:
1. Hire a pet relocation company to do it, which will cost extra $
2. Do it yourself
If you choose the latter, it is very doable, just needs a bit of planning.
As shared by others, just thoroughly understand the animal entry requirements, and complete the forms and veterinary requirements in time, and make sure to plan ahead.
As for apartments, a great way is to actually work with real estate agents, and tell them you want a pet friendly apartment. They will do all the work and provide you will lists of potential ones. Just browsing through the real estate websites that allows you to filter by 'pet friendly' may be misleading, as many owners are ok with pets or can be negotiated to be ok with pets, will often default as not allowing pets. Even the current place we are renting now did not officially advertise to be pet friendly. But we met with the owner, had a good rapport, and the owner was ok with it.
One thing to note is obviously lifestyle. Homes can be a bit smaller. Depending on where you live, there may be less grass. One thing that dogs will need to get use to is to do their business in concrete road instead of grass. It took our dog maybe 3 days to get use to it
Hope this helps