Best use a rail planner like the one of Deutsche Bahn or ÖBB. These are my results on DB that seems convenient, with connections that are not too tight

Be aware of the mandatory reservations on the Freccia trains in Italy. You can get these via the ÖBB website. Do not choose seat reservations only for the Italian Trains, but continue like booking an ordinary ticket. You'll have to add the Eurail/Interrail discount under the passenger details. The reservation cost in Frecce (FR) trains is 10 EUR per seat. 

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Thanks very much for your response, Brendon. I’m in Graz now and am going to the station to ask them, as the sites you suggest give differing information- and conflict with your info above.

Will post some feedback when I have more clarity.

Thanks again though!

Ingrid 

Always trust the information on the website of the rail company itself. In this case ÖBB and Trenitalia. Deutsche Bahn (DB Navigator App or just the bahn.com ), the one I used, has also correct and up to date information for most of Europe)

The Eurail website and rail planner app are often wrong, since it only gets a monthly update.

Now, I didn’t pay that much attention while looking it up, so the transfers between trains are at least with 45 min time. But it won’t make a big difference, and you might want to stretch your legs after 5,5 hours in a train (Railjet) :)

Hi, I would not travel like DB Navigator says via Leoben because it takes longer, but it is on a train. You can use instead ÖBB IC Bus Graz to Klagenfurt instead - included in the pass (the ICB is missing on DB navigator). Reservation optional but highly reccomended. You can reserve a seat via oebb.at

Thanks very much for these replies. I’ve bought a ticket for the trip above Angelo. Good to know that the bus is also covered by the Eurail pass. 
 

There have been warnings about a rail strike in Italy on Friday. Wondering if anyone knows more? A friend will meet me in Brescia. Do I just wait and see?