@ZooYouthBen: 100% agreement on the topic focus. Constant grumbling about certain members is really not necessary.
About Papua New Guinea: depends on which species You take into account.
Some animals, like Southern Cassowary, the sugar glider, the New Guinea subspecies of eclectus parrot and crowned-pigeons are rather common species in zoos. Some of its birds and reptiles are common in the exotic pet trade. But other spectacular and interesting species are clearly not common in zoos and unfortunately don't have a "high status" among most zoo visitors-may it BoP, Tree kangaroos, parrot species like the Pesquet's Parrot, New Guinea Crocs or Sir David's Long-beaked Echidna. All in all, I think countries with a still (partly) existing megafauna are the most attractive ones in the searched sense.
Which makes me wonder-"high status" in regard to the (common) zoo visitor or the wildlife enthusiast? If the latter is meant, Ethopia, Eritera, already mentioned PNG, Aru Islands, Sulawesi, New Caledonia, Falkland Islands, the Philippines, Ecuador, Colombia, Costa Rica, Namibia etc. could also be mentioned.
@Jurek7: sorry, just saw that You already mentioned Peru.