Hopefully you'll never need a doctor in Vienna, but if you do I can highly recommend this company. Doc Around the Clock.
http://www.docaroundtheclock-vienna.at/
They were recommended by my hotel and Dr. Zouhar came quickly, spoke English better than me, was thorough, diagnosed quickly and gave necessary prescriptions (he then Googled the nearest pharmacy to take them to). You'll definitely want to have insurance to cover the cost.
It was around noon and he said he'd already seen 5 or 6 patients who were on vacation, they provide service to a lot of the Danube river cruise ships.
And related, here is info from the Embassy in Vienna about doctors