It's even more silly than that - a long story, but in summary: the colonial administrations did genuinely attempt to settle on adopting one standard gauge, but they couldn't quite manage to all pick the same one at the same time so ultimately they all ended up picking different ones.
By my understanding: biggest single factor in the above, the unfortunate doings between New South Wales; and Victoria / South Australia; in the very early days of Australian railways, in the 1850s. I find it a lamentable, but almost splendidly crazy, tale. If I have it rightly, initially all three colonies as they were then, were by agreement, to use four-eight-and-a-half standard gauge (seeing eventual linking-up). New South Wales then hired a new chief engineer -- Irish, I believe, so a great proponent of 5' 3": he persuaded the new rail administration to switch to said broad gauge. In order to stay in line and still have a unitary gauge, Victoria / South Aus. scrapped their initial standard-gauge material, and recommenced with 5' 3". NSW's chief engineer then left, after only briefly holding his post; and was replaced by an Englishman who was an even keener proponent of standard gauge, and who managed to make happen, a switch back again to standard gauge. At which point the two south-eastern colonies said in effect, in the local idiom, " ****** this, sport -- it's becoming totally mad. We're bloody sticking with 5' 3" now, and let the chips fall where they may !" And so things proceeded.
It became an issue far sooner than might otherwise be thought; the first meeting of different gauges (4' 8.5" from Sydney and 5' 3" from Melbourne) occurred in 1883, and the second (4' 8.5" from Sydney and 3' 6" from Brisbane) in 1888.
I gather that 3' 6" gauge coming additionally on the scene, made at any rate more sense than did the above business between the wider gauges -- 3' 6" was thought more suitable for (meaning no offence here) the wilder / more remote / more marginal parts of Australia. There's a highly "compressed" account of "three-gauge Australia -- how come?" in the book on Australia by Bill Bryson -- who basically looks with favour on rail transport; but being essentially a layman, not a railway enthusiast, he rather often fails fully to "get it" re railway matters. Having listed the three gauges with a brief hint at "how, where, and why": Bryson (always on the look-out for a poking-fun opportunity) writes: "South Australia, inventively, had all three." Which has indeed been the case; but not through mere weirdness. S.A. started early on, as above, with 5' 3"; as time went on and railways were projected in S.A.'s more outlying parts, 3' 6" gauge was used for such lines -- an understandable enough choice. In the early-ish 20th century, the Commonwealth Railways' standard-gauge line linking South, and Western, Australia came into being (opened throughout in 1917, I think).
It was finally agreed (or perhaps re-agreed?) in 1921 that 4' 8.5" should be the single standard for interstate lines.
en.wikipedia.org
Most interesting link; thank you. Attention particularly engaged by the map illustrating the suggestions for gauge-standardisation, of the 1945 Clapp Report. Interesting, that this project envisaged wiping-out of the 5' 3" gauge, all to be converted to standard; but retaining most of the 3' 6" in the wilder areas. Also, its seeing a standard-gauge link being created right up north to Darwin -- not, as has occurred "in real life", per standard-gauge up from the Trans-Australian route, north to Alice Springs and then to Birdum and Darwin: but with new construction way inland, starting-point Bourke in N.S.W., running northward into and through the Queensland outback to a meeting with the existing 3' 6" Townsville -- Mount Isa line; this line being converted throughout to s/g, plus new construction north-west from Mount Isa to Birdum -- southern terminus of the then Commonwealth 3' 6" line from Darwin, which would be standard-gauged. Some fascinating might-have-beens !