Expat Health Insurance
Cigna Global Health Insurance.
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Discovery Bay or another one of the outlying islands is actually best for dog ownership, but that's the ideal talking.
Do note that you're not allowed to bring dogs on public transportation in Hong Kong, except on ferries and in private taxis.
It will roughly cost you 500 HKD to import your dog to Hong Kong. You say you don't need to quarantine your dog, but double-check this, depending on where your dog is coming from, it may be required.
In China you are allowed to import only one pet per Z visa (work visa), but Hong Kong is a special administrative region and so has different visa laws and customs regulations. I know you can bring more than one pet with you, but I'm not sure exactly how many the limit is (I assume there IS a limit and you can't import an entire farm of animals!) The problem is your accommodation is likely to be smaller than it is back home, so you should think about whether your pet(s) will be able to cope with less space.
Have a look at Shipping and Removals in Hong Kong for more about moving pets to Hong Kong.