You can connect to your train as late as 13:47 using the S-Bahn from the airport Regionalbahnhof. It is a local transit ticket and the trains go every 15 minutes and get you into the station in the underground level in 11 minutes.
If you are running late, you can get the 14:01 IC train from the airport Fernbahnhof for 8 EUR also in 11 minutes and bring you into the station on Track 1 and your Vienna train departs from Track 4 so you should have enough time to make it.
I don't see a taxi getting you there any faster than 11 minutes, in fact you won't even get outside the airport in that amount of time.
Have you bought the ticket yet? If not, just buy it using Frankfurt Airport as the start point and the train connection will be included in the price.