Given Majapahit's feudal nature, I'm not sure that they will build Australia. Maybe they'll just fund it, and corruption will run rampant in this colony.
Also, the whole of Australia is just difficult to defend. Even if Majapahit goes strong, it will probably end up like a second China.
Who says they'll go there any earlier then 1700s ?
I'm not sure it's any possible for Java to pull anything like Japanese or Chinese isolationism, meaning they'll be constantly exposed and informed of outside development. However they'll still be in more comfortable distance from Europeans compared to, say, the Ottomans. Perhaps it can be argued they'll end up the way Thailand did IOTL, or Zanzibar realm before being carved up into pieces, or on par with average South American countries of 19th century, but Japan was arguably rather close to turning into colony herself, and seeing the similarities between Javanese and pre-Meiji Japanese nature of statehood, and smaller size of area to build up upon, and proximity to much thicker money stream, it simply has better odds, and that is skipping the twice as long period to evolve before the dawn of European industrial imperialism.