Germany/Austria

7 days is too much just for Munich. If it were me, I would visit Munich for 2 days, then go to Nuremberg for 1 day with a Bayern ticket, Füssen and Neuschwanstein Castle in 1 day, again with a Bayern ticket, then go to Salzburg and stay there for 3 nights, spend 1 day on the Salzburg trip and 1 day on the St Gilgen boat tour, also there is a direct bus from Salzburg to Konigsee in 1 day. Then I would go to Vienna.

And Prague is a 4-hour train trip from Vienna, so it’s doable within your timeframe.

Yes, Prague is definitely worth seeing and a relatively short train ride away from Munich. Budapest is another idea in the east, but farther than Prague. If small town Germany would appeal to you, I strongly recommend Bamberg in the northern part of Bavaria state. It features great cultural sites -- beer brewing museum, ETA Hoffman museum, great bicycling opportunities -- in a city of only about 75,000 people. Count von Stauffenberg, the German officer who nearly assassinated Hitler in 1944, was from Bamberg. I believe his palace outside the town is open to tours.

I honestly liked Munich and had enough to do there for the 4 days I was there. However, you can do the Munich Prague Vienna trip that Rick has in his guidebook but return to Vienna the night before.

I loved Munich and the Bavarian countryside and if you like beer, there are some breweries that you can tour. Weihenstephaner Brewery is in Freising. A lovely university town worth touring not just for the Brewery. I loved Munich and just hanging in the Englischer Garten, going to the museums and exploring some of the neighborhoods outside of the Altstadt.

A week isa very long time to stay in Munich. There are so many other places to visit in Germany, not all cities. If you read some of the posts on this forum you can get other ideas for places to visit. A nice easy cheat to start a trip plan is to look at what Rick offers for tours and pick and choose from that.
I noticed that a recommendation was made to visit Weihenstephaner. I second that enthusiastically.
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I think 7 days in Munich is a great idea. It is a great jumping point for many day trips.

You can take day trips by train to Salzburg, Nuremberg, Innsbruck, Regensburg, Garmisch/Partenkirschen to the cable car to the top of the Zugspitze, Bamberg, & Würzberg.

Depending how far along Oktoberfest is when you visit, lodging in Munich is likely to be very expensive unless you are hitting the tail. If not, then I'd head for Prague for a few days and you can continue on to Vienna from there.

A friend suggested that we rent a car and drive to the Dolomites.

Bad idea. Brenner Autobahn is under construction. Partly only one lane left open. Traffic jams likely.

Have a look at smaller Bavarian towns such as Bamberg with World Heritage old town or Regensburg.

If renting a car: Ensure to have driving permission (see regulation for Germany). Basically a valid driving license plus likely an IDP.

staying in Munich for seven days

How many days do you plan to attend Oktoberfest and what museums, sites, etc. do you plan to see in Munich? Do you have any day-trips planned with Munich as your base? If you don't know what you plan to do to fill those seven days, I would look at reducing your time in Munich.

If you enjoy Oktoberfest, consider going to Stuttgart. They have a similar festival around the same time. About half the size of Oktoberfest and a great experience.

Prauge is a great option. As others have suggested, head there from Munich and then end your trip in Vienna.

Have a great time.

You can get to all these places easily by train, without the hassle of a car. It's not like the US where cars are about the only way you can get around without flying.