The first Europeans to see Australia are normally considered to be Dutch Captain Willem Janszoon and his crew on the Duyfken in 1606, but there are also claims by the Portuguese to have discovered it first, somewhere between 1521 and 1524.
Even though the Dutch did name what is now called Australia as New-Holland, they did not colonize it. The main reason behind it is that the Dutch East India Company (VOC for its initials in dutch) was the one in charge of creating trading posts, they only made settlements where it seemed profitable: spices were the main resource they were looking for, they didn't find anything of that sort of on Australia, they also didn't find anyone to trade with, so they didn't create settlements there.