Bonnie,
I wouldn't suggest using Rail Europe for checking train schedules, as they typically don't show all solutions. Using the Bahn.de website and 24 June as the travel date, there appears to be a direct RailJet departing Venezia Santa Lucia at 09:55, arriving Wien Hbf at 17:35 (time 7H:40M). That train also stops at Wien Meidling prior to arrival at the Hbf. That solution is also shown for 1 July.
With advance purchase tickets, it may be less expensive than a flight and will most surely be a much more pleasant trip. When all is considered, there might not be much difference in travel time between the train and a flight.
That trip appears to be available now on the www.trainline.eu website for €29.00 PP! However there are conditions.....
"YM 1 International Sparschiene Italien Tarvisio: Strictly non-exchangeable and non-refundable."
Choose carefully before you hit the "Buy" button!