No. it's not clear. What evidence is there that Australia was one of the last to join the World Government as opposed to Crusher picking a country, any country, at random and she happened to say the first country that came to her mind starting with the letter "A."
What you quoted is crystal clear and cannot be argued: Australia was among those that had not yet joined in 2150. Crusher stated this historical fact in unambiguous terms. There's no squirming out of it, other than decisively taking the stance that Crusher was lying for no good reason, incapable of speaking English, or making an obscure joke.
What you say above is completely beside that point. It merely touches upon the second part of the issue: was Australia one out of a grand total of two nations to join in 2150, or out of 200? If the UE came to existence no sooner than 2150, then Australia was not particularly late to the game; if the UE existed before 2150, it means some other nations must have joined earlier, painting Australia as more reluctant to join than those others. Doesn't mean much if 187 other nations also "held back". Means a lot if just three others did.
Nuances to this: hundreds of nations remaining might still mean a more or less united Earth if those were small nations and the UE covered most of the globe and its population already. Australia represents a big swath of said globe, but might not represent much of the population even in 2150. But saying "no" for decades becomes the less likely, the bigger the players that have already said "yes" and are now looming over the others on this.
Well someone had to be the last to join
And that's the untrue thing: everybody could have joined at the same time. So, did they? The mention of a UE before 2150 might suggest not.
Timo Saloniemi