Last Minute trip feasibility

Of course it's feasable. I just started planning a trip that starts in the middle of October and runs through the end of the year. When I say started, I mean I'm still figuring out where I want to go in Europe.

Instead of renting a car from Berlin to Munich why not stick to trains. The German rail network is extensive you can easily find places to stop between those two cities. (If you like history, consider Nuremberg.)

And from the train, you can look out the window and enjoy the scenery. Not easily done when you're driving a car.

The train from Munich to Brussels is at minimum 6.5 hours long with multiple connections. I was going to suggest going from Frankfurt and then Berlin but the trains from Berlin to Brussels are about the same as the ones from Munich.

Totally feasible. What is your interest in Brussels? It's not all that close to your other cities. There are lots of fantastic places around Berlin, Munich and Paris. Off the top of my head, Dresden, Salzburg, Strasbourg, Tours, and I've not been to Frankfurt, but I've heard its a great city to visit, and there are interesting cities close to Frankfurt (Koblenz, Bingen, other Rhine cities). Your selected cities are all quite big.You might enjoy having some smaller cities in the mix.

SInce its your first trip, I would do all trains.

I agree with jules m-I don't see how Brussels fits your interest in culture, history and natural beauty. I would spend that time in Germany or France. I have been to Brussels because it was on the way to Ypres, but found it to be a complete waste of time. I loved Fussen. The small museum there is interesting.

Badbie,
Congratulations on your first trip to Europe! Don't worry about last minute. I agree with Jules and cala about Brussels. Compared to Bruges and Ghent it is a disappointment.

If I am guessing correctly, you will leave the states on the 8th and fly back on the 28th. Is that correct? If so, you will have 19 nights there. (Arriving on the 9th). You might want to spend that first night in Frankfurt to adjust to the time difference and get over any jet lag. Or with good train connections, then, yes, go straight to Berlin. Stay 3-4 nights. (That is just 2-3 full days.) The drive to Munich from Berlin takes 7-8 hours and takes you through Nuremburg, where I would definitely stay 2 nights. Munich deserves at least 4 nights (3 full days), IMO. Turn in your rental in Munich. This uses up 10-11 nights. I would skip Belgium this trip, but if you go, fly and spend your time in Bruges, not Brussels. Remember you have lost a day to travel between Berlin and Munich. Of course, you will experience Germany as you drive. You will use a day after Munich either going to Belgium or to Paris. Personally, I would use all the days left In Paris.I consider it to be the capital of Europe and an unforgettable experience!

So, to recap (just my suggestion of course).....
Nights 10/9-10/12 Berlin (3 full days)
Nights 10/13-10/14 Nuremburg (remember most of 10/13 will be driving from Berlin to Nuremburg, so 1 1/2 days)
Nights 10/15-10/18 Munich (you will arrive before noon, so 10/15 will be almost a whole day there, so 3 3/4 days)
You can turn in the car on arriving in Munich unless you have plans for some side/day trip from there. Otherwise turn it in when you leave Munich.
Nights 10/19-10/22 Belgium (fly from Munich to Belgium on 10/19, so 2 full days there...travel on the 19th will take up a good chunk of the day) Train to Paris on the 23rd, about 3 hours.
Nights 10/23-10/27 Paris (4 full days, plus part of 10/23 after a 3+ hour train from Belgium)
Day of 10/28 fly home.

IMO, Paris deserves the most time, so this trip I would skip Belgium and fly to Paris from Munich. But that's me.
Please remember, this is YOUR trip. I just highly recommend figuring out the method and time involved moving from city to city, and counting nights, which lets you know how much you can do and see. With that advice, I defer to your wishes.

Bonne chance and bon voyage!

I suggest you get a copy of Europe thru the Back Door for your first adventure. It is full of great advice. Advice such as getting a business card from you hotel, take it from experience as we got lost in Strasburg and couldn't remember our hotel. This was before cell phones. I totally obscenely over packed now can go for three weeks with an overnight bag. Also remember we all had our first trip and mishaps and lived to return to Europe. Also ask for help on this site using the country specific sections for advice on hotels, sightseeing, restaurants. etc. So exciting for you. Just the magic of it all!!! Good luck.