Australia and USA Populating at the Same Rate: Coincidence?

I wondered: how does Australia's current population density compare to the U.S.'s at the same point in its history? Australia's first colony was founded in 231 years ago in 1788; the future U.S.'s first continuous colony that was a center of population expansion (i.e., Jamestown, not St. Augustine or Roanoke) was founded in 1609.

Today, 231 years after its founding colony in 1788,* Australia has a population of 25,203,198, giving a population density of 7.93 people per square mile.

In 1840, 231 years after its founding colony in 1609, the USA had 17,069,453 people. Taking into account its size at the time, the U.S. had almost exactly the same population density with 7.92 people per square mile.

Interesting, but possibly coincidental. The first observation to make is accessibility: from the period 1788 until today, it's much easier to get to a new land and spread out from one's landing location than it was in the period 1609 to 1840. Australia is also further away from Europe. Had Australia been settled at the same time, I doubt it would have filled as fast. There also seems to have been more reproduction with natives in North America, and also a denser native population (for the continent, an upper bound around 20 million is often estimated, versus Australia with 2 million.)

Related to its lower pre-colonial native population, Australia is also not as innately hospitable as the U.S. Large portions of the coast are inaccessible swamp, and a massive portion of the interior is desert with poor soil. Because the coasts are much better, Australia's population in 2019 is 86% urbanized, versus 10.8% in the U.S. in 1840.

Related to not being as hospitable, Canada is the obvious comparator. Canada at a similar point after its first colony had a density of 0.29 people per square mile, more than 27 times lower than the U.S. at that time, despite beyond as close or closer. (It's still 8 times lower today, despite having a 5-year head start.)


*I'm not counting the ancient Indian contact with Australia, which is now genetically confirmed. It turns out that's right around the time dingoes appeared - likely not a coincidence.