There was a major report last year into a Brisbane-Sydney-Canberra-Melbourne proposal.
This would certainly be possible, but it would be such a big job (a credible claim to greatest railway construction in history) that no government would ever be able to commit to it. It would take approximately 45-50 years to build, and before anyone laughs at the timescale that's still a kilometre/year construction rate of over twice the rate at which the high speed line from Folkestone to London was constructed in considerably easier terrain.
The terrain is very tough - the plumbline from Melbourne to Sydney is about 700km long but goes through terrain up to 1,600 metres above sea level. The shortest remotely practical high speed rail route would be about 820km long, and even that would require many long tunnels.
Ive done the Melbourne to Sydney trip by rail and yes it takes 12 hours but it goes through some barren outback as do the rest of the lines.
Given how cheap and quick flying is between these cities is there any reason at all as to why you would want to spend untold billions building new lines trhough the desert and still be unable to do the journey quicker than by plane?
You must be thinking of the Sydney-Adelaide-Perth route with regards to the desert, there is no desert between Melbourne and Sydney. The train time is still around 12 hours largely thanks to the winding alignment through the Great Dividing Range and various terrain issues which would be extremely expensive to solve when the demand simply isn't there.
A 320km/h line on a 850km route could provide a transit time of around 3.5 hours on a full express run. This would be a quite competitive centre-to-centre time against air, and having a stop of the outskirts of each city (e.g. Broadmeadows in the north of Melbourne and Campbelltown in the south-east of Sydney) would provide even better transit times for many people than having to battle their way to/from the city centres at either end of the high speed journey.
The real benefit would be to freight transport. Lots of trucks use the Pacific Highway (Brisbane-Sydney) and Hume Highway (Sydney-Melbourne) for intercity runs. These could be put onto Eurotunnel-style roll-on-roll-off trains at terminals on the outskirts of the major cities which should be able to cruise at 160-200km/h. At the moment, rail simply cannot compete on Melbourne-Sydney general freight because the line is too slow and there's too much time wasted at the container terminals at each end, but a roll-on-roll-off service would allow that time to be cut down.
And how would they deliver the electricity over the vast distances and how far is too far for said electricity before it becomes more environmentally friendly to go by train?
This would only be a problem for electrifying to Perth.
Brisbane-Sydney-Canberra-Melbourne and Adelaide-Melbourne wouldn't be a problem, and in the case of Adelaide-Melbourne the rail corridor is actually shared with major transmission lines for about 250km of its length.
Solar energy must surely be a no brainer in Australia, given there is such a vast area of uninhabited land and a small population.
Solar thermal would be possible for the outback sections of the Trans-Australia Railway, if it ever turns into a mature technology. Photovoltaic cells would be no use at night, and when even an impossible 320km/h line would take ten hours you can't afford to have the line open only during the day.
The Trans-Australian Railway is 1692km from Port Augusta (SA) to Kalgoorlie (WA), including the famous 478km straight line which covers 4.3° of the earth's curvature. Both Port Augusta and Kalgoorlie are also the end of the line as far as the National Electricity Market and Western Power transmission networks are concerned. The railways could set up their own transmission lines to serve the line for a couple of hundred kilometres out from each end, but beyond that there would need to be purpose-built power stations.
Even if you set up new power stations, that wouldn't solve the issue of double-stacked containers and electrification being incompatible, or the issues with trying to maintain an electrical system in such extreme weather (shade temperatures in the day of 40+°C and overnight minimums below freezing
on the same day) or the question of who in their right mind would want to pay for it.
The Trans-Australian Railway is fit for purpose as it is - it carries 88% of the land freight crossing the Nullabor Plain and 115 km/h is a good speed which gets close to the optimum transit time - any faster and the minimal time gained would be lost in extra fuel stops, assuming it wasn't lost waiting at crossing loops. The rail distance from Melbourne to Perth is about 3,400km - if a 320km high speed line the whole way was possible (and if the train could actually run at full speed the whole way, which is not realistic) it would still take about 11 hours for what is currently a four hour flight depending on the wind direction.