The train trip from Austria to Switzerland is long but is quite beautiful. You go lengthways through the Alps. The highest point is the Arlberg tunnel. See here for more info: https://www.seat61.com/international-trains/trains-from-Vienna.htm#Vienna-Switzerland
In Luzern (local spelling), go up one of the 3 local mountains (Rigi, Pllatus or Titlis), railways and cable cars will take you to the top of all three. Titlis is the highest and has a small permanent glacier at the to you can visit, see website: https://titlis.ch/en
For a rail trip take a train from Luzern to Interlaken for the day. This is the "Brünig Pass line" and is very scenic. Info here: https://www.zentralbahn.ch/sites/default/files/Faltflyer_LIX_2017_e.pdf
October will be in between seasons, a bit late for the summer season and much too early for skiing. You might find it a bit chilly coming from Australia.