There's a direct Eurocity in the morning and a Eurocity/Intercity connection with a change of trains in Maribor. Both take about 6 hours and go via the scenic Semmering Railway. No reservations needed! 

I usually use the DB Navigator app alongside the Eurail planner, because they seem to be more up-to date. (or go to the website of German Railways: https://www.bahn.com/en)

And since last week the direct Eurocity from Vienna to Ljubljana goes even further to Trieste (Italy)

Yes, that's truly awesome! Connections between Italy and Slovenia have improved a lot in recent years. I remember only a few years ago you had to go via Gorizia ...