Woodie,
I think one of the reasons that there were/are so many American railroads is because they were private endeavors. For example, when the need for a railroad between two points arose, the first group of investors who could raise the money built it. The result was that there were numerous small, privately owned lines, many of which merged into larger companies as a matter of econonic survival. Union Pacific and Burlington Northern Santa Fe, for example, are composed of many smaller railroads. (Some railroads started out big, though.)
Some railroads were built by government bodies. The State of Texas owns at least one railroad, the Texas State Railroad Historical Park, which was originally called the Texas State Railroad. It was built to service an iron smelting plant operated by one of the prisons. It now runs daily excursion trains between the towns of Palestine (pal-es-steen) and Rusk (where the prison was located).
The U.S. population is considerably larger than Australia's (imagine the population of the State of Texas spread over the entire continental U.S.), so there was/is a greater need for more railroads!
-Rory