That's an interesting question. Not one that I am an expert at to easily come to an answer with a highly adaptable, cosmopolitan genus of rodent. In talking about the future of a continental fauna following the fortunes of the conditions outlined above, my answer would be an educated hypothesis, since such an opportunity has not been actually attempted, nor possible at the time scale suggested. But that hypothesis is based on established evidence and not for a desire to see a specific outcome that is often the case in arguments for creationism.
For those that demand creationism and use biased arguments founded on flawed logic and information, take note. The first thing I did in formulating my answer was to look to what we know from SCIENTISTS that study things like rats, speciation, Australia, animal ecology, extinction and related subjects. I didn't go to AIG, Wowie! Creationism dotcom, Pseudoscience and Denialism for Beginners dotcom or any other biased source whose goal is to get you to think like them through intellectual dishonesty rather than provide valid information for viewers to draw their own rational conclusions. I didn't stare out my window and watch squirrels and imagine my facts into existence.
I'm trying to keep this as short as possible so as not to swamp others with repetition of a needless, pretentious and overwhelming volume of information provided solely to obfuscate, confuse and mislead.
Here are some links from Wikipedia that provide a good summary of rat history, taxonomy and biology as well as condensing down other information much better than I could in the space and time required for an answer.
Rodent - Wikipedia
Rat - Wikipedia
Tanezumi rat - Wikipedia
This links to a paper discussing invasive species in China that is of use in understanding the subject.
https://www.researchgate.net/profil...82a/Invasive-species-in-China-an-overview.pdf
As a group, rats are a highly adaptable mammals capable of existing in numerous niches. That they are is evident in the radiation of species throughout the globe. Particularly, the group of species that have reached pest status through their adaptive capacity. The species mentioned are omnivores and can survive on almost anything they can find to eat. Rat species already exist in Australia and have for about a million years according to the fossil evidence.
According to the literature, rats from Shanghai would most likely be
Rattus tanezumi or
R.
norvegicus. Both are highly adaptable, wide-ranging species. There is a bounty of information on these species and their habits from decades and centuries of observation.
The criteria provided form the basis of an adaptive radiation of a species into numerous empty niches. That species would be isolated on an island continent under high selective pressure from the existing population of reptiles that include 140 species of snakes, many of which are venomous.
Australia - Wikipedia
Adaptive radiation - Wikipedia
Snakes of Australia - Wikipedia
Based on all of this, I would not expect the introduced rat population to have remained a single, static species. It would be the seed population for numerous speciation events to fill the available niches left with the removal of all mammals. Even after a million years, the original species is not likely to have found so stable a niche as to achieve species-level stasis. The Coelacanth of today is a member of a group with high morphological conservation due to the stability of the environment in which it is found, but that doesn't make it the same species as those of millions of years ago. Even in stasis, evolution continues on a smaller scale.
Coelacanth - Wikipedia
There are known examples of such radiation occurring from a small population of starter species to over 700 descendant species. The cichlid superflock of Lake Victoria in Africa is one example where even higher taxa have evolved.
Cichlid - Wikipedia
Speciation - Wikipedia
Some of the resultant species would likely be species of rats (though not necessarily or likely the original rat species) that fill those available niches that support rats. But the selection of predation, inter- and intraspecific competition and the changes in the Australian environment over as much as 20 million years, would lead to entirely new species of mammals and higher groups that do not exist today. Rats would still be rats if they exist there at all, but that simple dismissal would have been left well behind for the same reasons it is meaningless today.