Any decent kennel in Australia will have a list of requirements for importing dogs to any country.
From what I can remember from bringing our dogs from Dubai in the UAE to the DR you need a health certificate which must not be older than ????? weeks and a rabies etc. certificate which has to be older than ???? weeks! The actual import certificate we got at the airport in POP as the dogs arrived, from the vet at the airport, it was easy really.
For better info suggest you contact the vet Dr Bob Amelingmeier on the North Coast -
agape@codetel.net.do - he should be able to point you in the right direction.
Australia to the DR? One hell of a trip for the dog!!!!