Too Much ?

First thing...flying in from far away (overnight, redeye flight?) and upon arrival, then jump in a car and drive off into a foreign country is not a safe or wise choice (I've done it myself, and I probably shouldn't have). I get the notion of pressing on to your actual destination, but why not do the train to "the Rhone area" (very train-friendly), get a good nights sleep, and pick up your car the next day, when you'll be in better shape to drive and live through the day? Please consider the risks to yourselves and others.

I agree that you could be careful driving right after a transatlantic flight.

I do it all the time, but I am always so pumped up and excited about our trip that I am never tired. Also, I never plan to drive much the first day.
Each person needs to evaluate your own ability in this area. If you do drive the first day, don't plan on going far. For example, landing at Frankfurt, if you drove to Heidelberg that would not be far. Most of your drive would be on the autobahn.

Your plan is OK, but not sure why you want to spend two nights in Rothenburg. You can see that city quite well in one day.
Don't miss the Romantic Road medieval towns like Dinkelsbuhl, Donauwurth and the great city of Augsburg.

Except for the possibility of impaired driving on Day 1 it's surely feasible. I probably wouldn't want to pay the car drop-off fee that one normally pays for dropping in a different country. You should probably look into that first.

2 nights Rothenburg (maybe 1 and add the day to Bavaria area) 3 nights
Munich/Bavaria area (arrive after Octoberfest to avoid costs and
crowds). More interested in the countryside.

You probably shouldn't mention or consider Munich if you are interested in the countryside. Munich is a large, spread-out city.

Rothenburg doesn't require a lot of time.

The "Bavaria area" is bigger than you are imagining it. It's not just a small area around Munich - it's huge - and you will cross into Bavaria very soon after leaving the "Rhine area" (which is in the "Rhineland Palatinate") for Rothenburg. Here is a map of Germany showing Bavaria in red. And here's a map of Bavarian cities and towns.

We have always rented cars in Europe and have never used the train
systems. I guess we always found the car more flexible and it allows
us to go off the beaten path.

Your itinerary is essentially the beaten path. I would look around a bit more before you start booking rooms. If you want to go OFF the beaten path, consider your itin. a first stab, and do some more research using other materials besides Rick Steves'. EVERYONE knows about Rothenburg (which exists now only for tourists) and the Romantic Road, and that's where you'll find everyone. Not that these are bad places. But they are not "the road less traveled." There are MANY nice and interesting places between the Rhine and Austria that you can explore. You should find your own, based on your own interests; they won't be unknown or tourist-free places of course - just a bit less well-known. Here are just a few examples of places that aren't "front-and-center" in the typical guidebooks.

Sommerhausen

Iphofen

Bad Windsheim

Pappenheim

Miltenberg - and a visitor's guide.

Mittenwald - and a visitor's guide

I hear statements like yours about cars and trains quite often. But it is not possible to draw conclusions about the flexibility or inflexibility of train travel when you've never done it and don't understand how it's done. I have to assume that the opinion is based more on one's love of driving than on the reality of train travel in Germany (which is extensive, efficient, and inexpensive - and also offers lots of flexibility.) And that's fine - if you enjoy driving, do what you enjoy. I've driven in Germany, but the rail system is so good that I now do all my exploring by public transport (which has taken me to the places above as well as many others.) Also worth noting: if you enjoy beer/wine, you have the flexibility to come and go at will on the trains. DUI thresholds in Germany are very low.

You do need to spend one night in Rothenburg so you can do the Night Watchman's tour.

I don't see a problem with your itinerary car wise. I drive my own and I'm not very familiar with rental and train. The car option allows you to go off the beaten path even more as you know. Know ahead where you are parking though. October can be a dead month in some places in the Nebensaison, so do a little homework. I remember visiting the Rhine area in October 20 years ago and things were closed and dead. Probably changed since then. Some of my favorite Gasthaus in Oberbayern take a pause too. Allow some travel days flexibility for bad weather if you are looking at visiting sights that are best in good weather. I like the Weinfranken, Altmühltal and Bayerische Hausberge regions too.

Wow, awesome suggestions by all. Good tip on places being closed/dead in October, never thought of that. I remember being in Italy on our honeymoon 25 years ago. Funny, we went with no hotel reservations except in our first location of Rome. We just found places on the fly in Siena, Venice, Verona, Lake Como, and Milan. We are the only people in the one hotel in Lake Como. It was actually great, the weather was warm every day and no crowds. I would imagine Italy is crowded most of the year now? Nice to be young and adventurous.
Thanks.

We are a couple, and always have reservations for the first 1/3 of the trip. After that, we do 3 days in advance. We still find inexpensive but pleasant accommodations.

As to train tix, they can be very cheap. rome2rio suggests that a ticket Munich to Salzburg would be 25-37 USD. So, 74 USD for both. Drop-off fee in a second country can be 300-400 USD. Economically, trains do it.

You sound like you are in your 50-60s. We used to do cars, but find that trains can do everything we need, plus we can drink some wine while we travel. And you get no speeding tickets nor do you get parking fees nor do you have disputes at drop-off time about the ding on the rear passengerside door. As Russ notes, none of your itinerary is off the beaten path. It's all on the rail lines.