MrMichael – VIE is a relatively compact airport and has prided itself for very short connecting times for years. It has been extended recently making some walks between gates rather long.
That said, if the inbound flight is a domestic or Schengen and pretty much first thing in the morning she might stand a chance – as does the luggage.
If the inbound is from a non Schengen destination she’ll have to pass through passport control, which can be busy with as little as one flight arriving and often just 2 desks open. Connecting passengers also don’t tend to be called forward at those desks.
If the transfer is later in the day the inbound aircraft may have picked up delays, eating into your 35 minute transfer, any weather (storms, snow etc) may add to this – although VIE is quite switched on.
35 min really does not leave any wiggle room – I’d go for a longer connection and enjoy the lounge (if eligible) or the Airest restaurant with its apron views – and a proper coffee and a slice of Sacher torte.