"Water buffalo's will propably survive in New Guinea, although keep in mind that just having a lot of domesticated animals is not neccesary to build to a great and developed civilisation, as the native American civilisations show."
The Peruvians raised llamas, alpacas, and guinea pigs intensively for their meat. To a lesser extent, they also made use of ducks and dogs, though the latter had largely been coopted for religious purposes. There is also limited evidence that they had begun to use chickens brought in from Polynesia even before the Spanish arrived. That's not to mention the fact that fishing was important for many of the cultures.
In Mesoamerica, dogs and turkeys were heavily relied on for supplemental protein. When the Spanish arrived, the Mexicans were backing this up with deer kept in pens (not really tame). They didn't really have enough of a protein base when you come down to it, and this was a recurring problem especially when soil depletion from corn cultivation peaked.
So yeah, domesticateds are key here.