Travelling via Athens Airport to Vienna

I'm not quite sure where you see a big problem here. So let's answer all the potential small ones:

When checking in you luggage in Doha show your boarding pass for Athens Vienna (you should check in on the web in advance!) and the check in counter in Doha may be able to check you luggage through to Vienna. Airport luggage handling is not tied to airlines. The EU is not the US, there is no rule that says you have to pick up your lugagge on entering the EU.
2h 45min should be enough time change flights.
Using seperate tickets is always a gamble. If you did this to save less than a hundred Euros it was not a smart move.

Michael Renper 455

Source: stackoverflow.com