Looking at this population map of Australia, it is easy to see where the main economic, political and cultural divide is likely to be in Australia. WA, or more accurately the south-west corner of WA, and all the inhabited lands east of the Nullarbor Plains. A division of the south and north won’t exist or will be minor as the north has an almost insignificant population.
The population limit of the north coast under both the industrial support system and industrial agriculture seems to be about 250,000, without those support structures the north coast’s inherent population limit is likely to be around 10-50,000. The north coast could support a higher population by importing food from either Asia or Australia and since its likely to be a trading hub the necessary wealth is well within reach.
An important feature is the massive disparity in size (in terms of populated land), population power and overall strategic importance. The west is a relatively small, weak, and sparsely populated outpost located at a strategic point along the clipper route. The east is the relatively large, strong, populous heartland that occupies a less strategic position along the clipper route, the eastern equivalent is occupied by New Zealand. While the west is likely to be an independent political, economic and cultural centre, and it will certainly be an important trading hub, it will never, for the simple lack of people, be the major half of Australia. It’ll be important, especially as it’s the first port after the Cap of Good Hope.
Another feature is the clipper routes affects on the east west divide. Since the route travels along the south coast and its unlikely for the wind currents to drastically change, there isn’t any effective way for trade to bypass one of the halves, especially since the sailing ships will need to be resupplied, and since its all open ocean, travel would be hard to cut off and none of the choke points of the Mediterranean exist in this part of the clipper route. The clipper route also connects the east and west far better (in terms of travel time) than most large (and some small) states have been throughout history; it took Rome months to move its legions from theatre to theatre, it took 6 months to travel the length of Archaemenid Persia, imagine travelling across Russia on foot or horseback. In terms of travel time, Australia isn’t anywhere near as big, it’s a 3 day train ride from Perth to Melbourne and the same rout by sailing ship is only a few days extra. Kingdoms carved out during decline periods have been bigger in travel time and almost all of them just subsumed the remaining governmental organisation. This isn’t to say that WA would necessarily stay united with the rest of Australia, having two separate governments is likely, but the cultures aren’t likely to wildly diverge and a Western and Eastern Australian is likely to have a similar (but not identical) worldview and cultural heritage.
The main variable is travel across the Nullarbor Plain, since that is the major land barrier between the eastern and western sections. The trans-Australian Railway (Kalgoorlie to Port Augusta) was finished in 1917 and its likely to still be operational for the next century and possibly after. The main danger to the Trans-Australian railway is that it will be merely maintained, instead of being retrofitted to deal with overshoot. If not, then as Australia slides down the path of overshoot, the land link will eventually be lost and the only reliable travel option will be sailing ships. So the variable is either having a strong transport link via sea and land or only sea. Communication isn’t likely to change either way, radio is unaffected, and unlikely to be lost, and it doesn’t matter hugely if a letter is a day or two later. How this could potentially affect unity is uncertain, these conditions haven’t existed before and are unique.