Coming in late, but to answer the original question, in the 1950s a train trip between Melbourne and Perth would have taken 4 nights and 3 days and involved
(1) Taking the overnight
Overland train between Melbourne (Spencer Street station) and Adelaide. This would have been a brand new fully air-conditioned train including sleeping compartments.
(2) Connecting at Adelaide to an afternoon departure on the
East West Express from Adelaide to Port Pirie, By the mid 50s this would have had new carriages to match the
Overland(3) Transfer at Port Pirie to the
Trans Australian. Two nights and nearly two days would be spent on this train which would have been all-sleeping carriages and dining cars.
(4) Transfer at Kalgoorlie onto the connecting train for one more overnight stint until arriving at Perth station early in the morning.
These were all well recognised and timetabled connections but it still would have been quite a slog.
Source:
https://www.comrails.com/library/timetables/TAR%20Psgr%20Timetable%20195301.pdfIncidentally, by the 1950s flying was also an option. TAA ran a daily Melbourne-Adelaide-Perth flight using a DC4 (later in the 50s a Vickers Viscount) taking about 10 hours. See
https://www.timetableimages.com/ttimages/tn/tn5310/tn5310-4.jpg