What is going to happen to me in Doha or Vienna Airport given the Coronavirus situation?

You have to transit in Doha, Qatar. According to IATA

QATAR - published 26.02.2020

Passengers who have been in China (People's Rep.), Iran, Japan, Korea (Rep.) or Singapore in the past 14 days will be required to self-quarantine for 14 days.

https://www.iatatravelcentre.com/international-travel-document-news/1580226297.htm

Although the rule doesn't specify about transit, there is a chance that you will be denied boarding. You need to contact Qatar airlines to make sure.

Austria doesn't deny entry to passengers from Iran, as of now. Although unlikely, it can change from now to your travel date.

The first thing you should do is contact your new employer. They may have procedures in place for any people coming for affected zones (China, Northern Italy, Iran...) to be isolated from other staff and/or the public.

It is difficult to guess what measures will be taken by the various authorities in Iran, Qatar and Austria regarding quarantine and isolation, or even outright travel bans, as this can change by the hour.

Qatar Airways have already cancelled 2 out of 3 of the flights from Tehran to Doha these last few days, and in the upcoming days.

Even if there are no bans or quarantines, and even taking into account switching to a larger plane and cancellations/rebookings, squeezing passengers booked on 3 different flights on a single probably means severe overbooking. Be prepared to be bumped off the flight if there are Qatari citizens or residents and/or premium passengers that need a seat on that plane.

The remaining flight on Saturday has been rescheduled to over an hour earlier. Add to that there will probably be lots of additional checks before boarding, and the fact that there will be overbooking, and you should be at the airport a LOT earlier that you would normally have, probably before midnight. You want to be the first in the queue. If online/mobile check-in is possible, do it as soon as it opens. You want your boarding pass to show "SEQ 001".

I suppose the rescheduling is to account for additional checks on arrival (as well as thorough disinfection of the aircraft after the flight) in order not to have issues with short connections.

Current Qatar Airways procedures for flights from Iran:

In line with various global and local health warnings, all incoming passengers from Iran and South Korea whose final destination is Doha and are showing no symptoms of the Novel Coronavirus will be asked to stay in home isolation or a quarantine facility for 14 days.

Passengers arriving from those countries who are showing symptoms will be transferred to the Communicable Disease Centre at the Hamad Medical Corporation.

So if you do not show any symptoms and are only in transit, you should have no issue boarding the flight to Vienna, unless Austria implements bans or quarantines by then.

Good luck!