We brought our black lab from the states to HK in the middle of March, and everything went very well with a pet agency in NY. For sure there is no quarantine required in HK for pets brought in from USA. Our dog detoured from USA to Amsterdam, since the agency told us they tried to keep the dog in the crate less than 10 hours flying on the air (did not relized it was because of the cost saving issue
).
I would say in general Hong Kong is a sort-of dog friendly place, specially with small sized dogs. But indeed here is a crowded city without free greenland for doggies. In considering this, we chose to live in the far-away countryside place with a backyard in Tai Po. Still I have hard time finding greenfield where dogs are allowed unleased besides hiking in the mountain area...
I heard there are a couple public areas / beaches for dogs. I only found Sai Kung Beach though.
Good luck for your moving.