The only reference to Australia that I even remember is that supposed we're the last nation to join the United Earth government, to which I can only roll my eyes and say, yeah, right. As if we wouldn't have jumped in as soon as the US and UK had joined.
Crusher was, in that scene, playing Devil's Advocate with Picard. She was arguing that full planetary unity might not be required for Federation membership. She asked him if Earth would have met the membership requirements if one of the old nation-states hadn't joined the United Earth government when it was formalized in 2150. Picard said that the analogy wasn't correct, but was cut off before he could finish his thought (he probably would have said that it wasn't correct because Earth was a founding member of the Federation).
Crusher simply picked a country at random. It wasn't intended to mean that Australia was in fact the last nation to join the UE government. It was just a hypothetical argument. It would be like me, as an American, asking if this country would have been allowed to be formed if Pennsylvania hadn't ratified the Constitution. That doesn't mean that Pennsylvania was the last to ratify; it's just a hypothetical situation.
FYI: Pennsylvania was the second state to ratify the Constitution. The last of the orginial thirteen colonies to do so was Rhode Island.
I've seen this issue of Australia pop up from time to time. I just can't understand why so many people continue to believe that Australia was the last to join.
Sulu was born in San Francisco, as he stated in The Voyage Home, making him an American, too, like McCoy and Kirk.
Also, from Voyager, Kim was from South Carolina, so that's another American character.
As for La Forge, I don't recall it being said that he was from anywhere on Earth. He was a Starfleet brat, so he was raised in many different locations throughout Federation territory. Just because he's black doesn't mean he's from Africa.
Correct about Sulu and Kim.
TOS had three Americans - Kirk (from Iowa), McCoy (from somewhere in the South), and Sulu (from San Francisco).
TNG had one American - Riker (from Alaska).
DS9 had two Americans - Sisko (from New Orleans) and Jake Sisko (most likely born on Earth's moon, but raised in New Orleans).
VOY had two, maybe three, Americans - Janeway (from Indiana), Kim (from South Carolina), and Paris (we don't know where he was born, but considering that his father was a senior Starfleet official, most likely San Francisco).
ENT had two Americans - Archer (from upstate New York) and Trip (from Florida).
Just for fun, here's where they were all born....
TOS:
Kirk - Iowa
Spock - Shi'Kahr, Vulcan
McCoy - somewhere in the American South
Scotty - Scotland
Sulu - San Francisco
Chevok - Russia
Uhura - never established on screen
TNG:
Picard - La Barre, France
Riker - Alaska
Data - Omicron Theta
Worf - Qo'nos
LaForge - the African Confederation
Beverly Crusher - Earth's moon
Wesley Crusher - never established on screen
Troi - near Lake El'nar, Betazed
Yar - Turkana IV
Pulaski - never established on screen
DS9:
Benjamin Sisko - New Orleans
Kira - somewhere in Dahkur Province, Bajor
O'Brien - Ireland
Odo - never established on screen (though most likely the first Founder homeworld)
Quark - Ferenginar
Jake Sisko - never established on screen (though most likely Earth's moon)
Bashir - never established on screen
Ezri Dax - New Sydney
Jadzia Dax - Trill
Worf - Qo'nos
VOY:
Janeway - Bloomington, Indiana
Chakotay - an unnamed Federation colony near the Demilitarized Zone
Torres - Kessik IV
Kes - Ocampa
Paris - never established on screen
Neelix - Rinax
The Doctor - Jupiter Station
Tuvok - Vulcanis Lunar Colony
Seven - Tendara Colony
Kim - South Carolina
ENT:
Archer - upstate New York
Trip - Florida
T'Pol - Vulcan
Sato - Kyoto, Japan
Phlox - Denobula
Reed - never established on screen
Mayweather - ECS Horizon, halfway between Draylax and Vega Colony