I recall some time ago reading something about this suggestion and the reasons why it was unworkable.
There were two main reasons if I recall correctly, the first being that there would need to be power to run pumps all along the pipeline because it was so long, and this wouldn't be possible as there would be too much loss running the power from the powerstations to remote pipeline sections. (Something to do with the loss of power over distance in the wires... I know it's not a high-tech explanation, but in lay terms that's what it is.)
I can't remember the second one, whether it was to do with the power and the length of the pipeline or what.... can anyone point me to something about this on the net?
Update: Received a long email from a commenter here who put his engineering hat on, here it is:
In principle anything can be done and when it comes to pipelines, I recommend having a browse through this site: The Golden Pipeline. I was unaware of this pipeline until I visited Kalgoorlie some years ago. It is an interesting story.
Now I will put on an engineer's hat and discuss for a moment the idea of pumping water south in the Australian continent. It is not the first time the idea has been raised, but here are the issues ( at least as I see them). Not in any particular order
The terrain over which of through which the water is to be pumped
The distance over which the water is to be pumped (hydraulic design - pipe friction losses, pump efficiencies etc)
The actual route across the country - fun and games with access, pipe locations, pumping stations, intermediate reservoirs etc etc
The energy supply along the route to power the pumping stations (it would have to be electricity)
The water supply and the nature of that supply, i.e., the water head and the end reservoir location
The design of the route which almost certainly would require storage reservoirs along the way to act as buffers and allow the system to be managed. Just think of a mass of water being pumped along a pipe - there are major control issues involved in shutting down the water flow if / when required because of the momentum of the moving water.
There would need to be a 'good' reliable water source (a dam) and there would need to be a decent sized storage source at the end of the line (another dam).. I'd have to guess that once these dams were built (and they would need to be properly positioned) they would be used where they were. It is most likely not feasible to design a system to collect storm water or monsoon water unless there was enough water and it could be channelled into a decent storage reservoir (a dam again) where it could feed into a pumping system.
Evaporation may be an issue for the exposed parts of the water system - intermediate reservoirs and to minimise evaporation the reservoirs would need to be either covered or built with a relatively small surface area.
Then there is the cost of the system and the cost to man and run it.
And finally there would need to be a use at the end point for all the water that is pumped.
Mind you I think this has been tried locally, e.g.how about the Ord River Scheme and it would be worth perusing that scheme to see why it has not gone very far. I don't know enough about it and have not put in any research but I have a gut feeling that it has not been viable.