Drive from Regensburg to Vienna, next to Danube

You cross the Wachau valley, one of Austrias highlights. The Wikipedia article is a good start:
https://en.wikipedia.org/wiki/Wachau

I would recommend a night or two there. It's really a lovely region.

Yes, it is possible to do this, expect it to take all least 6 hours without stops. So would suggest you include at least one overnight stop. Places to visit on route, include Bogen (pilgrimage church on hill overlooking town), Vilshofen, Passau, (Baroque old town, with stunning cathedral) Linz, Mauthausen, Melk, Krems, plus lots of little villages, (Obernzell has a nice little pottery and Schlogen, is a picturesque loop in the river). The roads are good in general, but can be fairly narrow in places and windy. Signposting is good, but expect to cross banks from time to time in order to keep close to the river. Traffic can be fairly heavy particularly around Passau and Linz.
The following links might be helpful
https://www.austria.info/uk/things-to-do/cities-and-culture/austria-europe-meeting-place/colourful-danube
https://www.bogen.de/default.asp?pid=5011
http://tourism.passau.de/Home.aspx
https://www.vilshofen.de/index.php/sehenswertes
https://www.mauthausen-memorial.org
https://www.linztourismus.at/en/lleisure/discover-linz/
https://www.donauregion.at/en/detail/article/13186-where-to-go-in-the-upper-austrian-danube-region.html

Places to visit on route, include

I'd like to add an important place to that list, namely Kloster Metten near Deggendorf and its magnificent Baroque library.

It might have just been the winter season but we loved a visit to St. Florian's Abbey (Stift) near Linz. From a Christmas week in Salzburg we visited St. Florian's and the Wachau Valley numerous times. The Wachau Valley had a great sense of quiet beauty about it.

I returned to the area in high season and found the traffic on side roads in the Wachau Valley to be a bit discouraging. I would guess that could be said of many places.