New Zealand has many peaks over 3,000m but very few reported incidences of altitude illness requiring evacuation, though frostbite is common on Mount Cook.
Australia’s highest point Mount Kosciuszko (2,200m) is an easy walk so is unlikely to cause altitude problems but it is still possible.
Papua New Guinea / Indonesia have a number of mountains over 3,000m, the highest being Puncak Jaya (Carstensz Pyramid) at 4.884m. Many tourists report AMS symptoms spoiling their trip and some trekkers have died. As with the African peaks it is worth trying to ascend more slowly and acclimatising if possible. The difficult tracks, lack of reliable maps, muddy wet seasons, limited medical care and risk of tropical illness can turn what looks like an easy weekend into a nightmare.
Borneo – Mt Kinabalu 4,101m can be climbed rapidly, resulting in a high incidence of AMS.
In 1982 two climbers were stormbound for two weeks on the summit of Mount Cook. When the weather improved, and they were rescued, both had suffered frostbite to their feet due to the combination of cold and altitude. Both men had their feet amputated. They have each returned since then to summit the mountain, with one of them also summiting Everest.