I know some of the private housing do allow dogs, but not sure which ones. But not the South Horizons. I have friends living there and that I do know for sure. Make sure your landlord will allow you to keep dogs as well.
As for the vet, DO NOT go to the one in Aberdeen. Been there once and wanted my Corgi's teeth cleaned. When we got home, we noticed that her big teeth were not cleaned at all!! They only cleaned the front where they were more likely to be seen. I had never gone back there since. To me, if they can't even do a teeth cleaning job well, how good they are for more serious cases??? This is just personal experience and my own opinion.
There are plenty of vets in Causeway Bay and Wanchai which are much better.
Hope that helps.