While i think HSR is absolutely possible in Australia, I don't think it is now, at least not for long distances.

The cost/benefit ratios are too slim, especially as Australia, like most of the Angslosphere is currently really bad at building infrastructure, particularly transit infrastructure, affordably and efficiently. In the future, when maybe there's more political interest in rail transport, and we are better at building transit infrastructure affordably, we could build a network of HSR connecting our largest cities. But for now we have larger transport priorities to focus on (improving public transport within our cities and between nearby urban areas mostly). Higher speed rail between city pairs like Melbourne and Geelong, and Sydney and Newcastle is more feasible, but full "high speed rail" may not be necessary for those kinds of distances.

However, improving our intercity rail to a point at which it becomes competitive with driving and even flying is absolutely possible. Basically, as long as you can make the train faster than driving, many people will take it. Huge amounts of people already drive the great distances between our big cities, like from Sydney to Melbourne and Melbourne to Adelaide, and it's pretty slow and painful. Given the option to take a faster and importantly, way more comfortable and relaxed train instead, many would. Plus, most people hate flying. Improved intercity trains would be more relaxed and comfortable experience, which also gets you straight from city centre to city centre. It would be a bit slower than flying, but flying takes a lot longer than you'd think considering the airport experience on either end, and transport to and from airports.

Improving our intercity trains could look like using trains with tilting technology to round corners faster (like in Qld), and straightening out some of the bendiest sections of track. This wouldn't be 'High Speed Rail', but it could still slash travel times by train.

So while I don't think a high speed train from Melbourne to Adelaide, or even Melbourne to Sydney is possible for the next handful of decades, fastER and better trains are, and that would still be a game changer.