It is unlikely but plausible that a Portuguese ship may have landed on Australia before the Dutch. However, there doesn't exist any concrete evidence to support that hypothesis. The theory originated with British geographers, and was not the work of Portuguese people faking maps to try and claim colonization rights.

Rather, it was initially based on the Dieppe maps, which were produced in France during the 16th century (with the oldest dating back to 1540). These maps were not produced to be used as actual maps, but rather, as works of art. They purported to show the entirety of the globe, though the entirety of it was not yet known, and so had to 'fill in the blanks', so to speak. Many of these depict a landmass roughly where Australia is today, and label it Jave la Grande. However, this landmass is usually connected to what we would call Antarctica, and not depicted as its own continent.

The name is derived from The Travels of Marco Polo, which was published in 1300. According to Marco Polo, the largest island in the world was located 1300 miles to the south of Champa. He was describing the island of Sumatra. However, a scribe at some point made an error, and it was published as 1300 miles to the south of Java - roughly where the northern coast of Australia is. And so, because of a scribal error, you had a book suggesting the existence of a large landmass roughly where Australia is, even though there was not yet any evidence of such a landmass, way back in 1300.

The continent of Antarctica had also not been discovered yet at this point. Nonetheless, the existence of a continent far to the south had been hypothesized since antiquity. Greek philosophers like Aristotle and Ptolemy argued that there was probably a large southern landmass on the basis that it would 'balance out' all the northern landmasses. There was no other evidence to support the existence of this hypothetical continent, which was known as Terra Australis.

During the age of exploration, basically every time a new landmass was discovered further South than anything else previously known, it was initially assumed to be the northern coast of this hypothetical continent, only for subsequent explorations to reveal they had just found another island. This happened a lot as various explorers attempted to find a Southern passage past South America. Most notably, after Ferdinand Magellan discovered the Strait of Magellan in 1520, the island of Tierra del Fuego was initially thought to be the Northern tip of the legendary Terra Australis (some suggested it was probably just an island as early as 1525, but it wasn't until 1616 that it was proven to be an island).

And so in 1544, Jean Alfonse suggested that Terra Australis did exist, arguing that Tierra del Fuego represented one end of it, and that the 'largest island of world' suggested to exist by Marco Polo likely represented the other end of it, and was thus not actually an island, but part of a yet-to-be discovered southern continent. Alfonse labeled this land as 'La Grand Jave' in reference to Marco Polo's description of it being the largest island in the world - and placed it roughly where Australia actually is, on the basis of the error made when scribes were making copies of Marco Polo's book, and the assumption it extended through the South Pole. This idea was then incorporated into the Dieppe maps, whose makers did not know what was there, and 'filled in the blanks' by assuming that Terra Australis existed and extended about as far north as the northern coast of Australia actually does (and a bit further on its western side, extending all but to the island of Java).

This is all to say that, at the time the Dieppe maps were made, they were almost certainly not considered to depict a discovered continent, but rather, to depict a hypothetical continent, Terra Australis, which was thought to encompass both Antarctica and Australia.

As your Dad mentioned, the Portuguese were the first to land on various Southeast Asian islands. They developed a stronghold in Malaysia in 1511, from which they explored the surrounding islands, but did not reach Timor until 1556. Thus, they were, all things considered, relatively close to Australia for some 50 years or more before the Dutch and Spanish expeditions of 1606. However, I agree with you that it would be a fallacy to assume that they would have discovered Australia within that time. 400km is not a small distance. Moreover, as far as we know, nobody ever claimed to have discovered a landmass further south. However, there were probably rumors of a land mass to the South of Timor, arising from the historical ideas of Terra Australis, and possibly from stories told by the natives.

Alternatively, this consideration might instead be taken as evidence that actual knowledge of Australia did not predate the depictions of it in the Dieppe maps, in that, the landmass was depicted there well before even Timor was reached.

The idea that the Portuguese had a secret colony there because they did not want to be caught violating the Treaty of Tordesillas has no evidence. It has been postulated only as an explanation for why the theory that Portuguese landed on Australia before the Dutch also has no (definitive) evidence. This is just a conspiracy theory as far as I'm concerned. At any rate, the Treaty of Saragossa was signed in 1529 and gave Portugal rights to all but the east coast of Australia. And so, if Portugal did establish a secret colony sometime between 1494 and 1528 - they could have announced their discovery at any point between 1529 and 1606 without violating the treaty.

Much later, in 1762, Scottish geographer Alexander Dalrymple first learned about the 1606 expeditions (in particular, Luis Váez de Torres' discovery of the Strait of Torres), and connected that with the idea of Terra Australis. He basically made the exact same assumption as Jean Alfonse made in 1544, which was incorporated into the Dieppe maps - maybe the land the Dutch discovered in 1606 corresponded to the northern edge of Terra Australis.

Dalrymple's ideas prompted a number of expeditions to determine whether the land mass genuinely corresponded to the legendary continent of Terra Australis, including James Cooks' expeditions. Cook's first expedition in 1770 mapped the East coast of Australia, and demonstrated that Australia was not part of Terra Australis. His second expedition in 1772 proved that New Zealand was not a part of Terra Australis either, and further, he circumnavigated the globe at a high southern latitude, demonstrating that any possible Southern continent was restricted to Polar regions.

As somewhat of an aside, it was because of this that the idea of a southern continent faded from favor. And in 1814, Matthew Flinders published the book A Voyage to Terra Australis, in which he argues that the legendary Terra Australis hypothesized to exist by Aristotle and Ptolemy in antiquity did not actually exist. He named the landmass that did exist - the next best thing - in its honor, as Australia. It wouldn't be until 1820 that Terra Australis would be discovered (what we now call Antarctica).

Meanwhile, in 1786, Dalrymple re-discovered the Dieppe maps, which seemed to be made prior to the discovery of Australia, and yet depicted it, if only as a protrusion of Antarctica. So he briefly mentioned the possibility of this being evidence of an earlier Portuguese discovery (the Dieppe maps were made in France but often relied on Portuguese source material and used Portuguese names for locations - such as La Grand Jave - which is why it was assumed to represent a Portuguese, and not a French, discovery). However, Dalrymple did not particular champion this belief, and it did not gain much traction until much later.

Later supporters of this idea generally suggest that the Dieppe maps were made with some greater knowledge of what the coast line of Australia looked like than could have been the case if they were just depicting a hypothetical continent (or else, they were ignorant altogether of the idea that it might just be depicting a hypothetical landmass). This approach often involves distorting the depicted lines to various kinds of map projections and trying to match them to the actual coastline of Australia, and is generally not very convincing. Most people believe the maps merely represent the landmass Jean Alfonse and others had hypothesized to exist there.

I'm not a linguist, but my understanding is that the evidence on that front is also not very convincing.