Traveling with a six month old is certainly doable, and in some ways a road trip is ideal. You have a car for hauling diapers and baby gear, you don't need to worry about baby screaming on a long haul bus or train, and you can stop when needed.
I've done US road trips with kids under 1, but my European travels with very small children basically involved going to 1-2 places and staying there for a week or more. So a week in London, then a week in Paris. That kind of travel seemed easier. You don't get to see as much in a day, unless your child is extremely flexible and happy to sleep in strollers.
2-3 days per place will be a lot of unpacking/packing and much less seeing the place than you may be thinking. Honestly, I'd cut the destinations in half. That would make for a much more rewarding trip. Also, really figure in travel times. Something like this - leave Madrid in the AM, 6 hours drive to Seville means arriving at 4PM (or whatever), then see how much time you actually have to see the destination. I think it will be less than you think.
My main advice for road trips in general is to budget more time than planned to get places. You might be really fast - a sleeping kid tends to entice adults to keep driving - but things like diaper blowouts or general fussiness can really slow you down. Plan in stops you child will enjoy. Infants aren't fussy, a park or nice walking path will do just fine. Make sure you have the sleeping arrangements figured out - cribs may or may not be available. A pack-and-play or other portable crib is great if you don't sleep with your baby. Baby food is everywhere, as is formula, but if your baby needs something very specific, bring it. Honestly, I breastfed and gave my child regular food mushed up (talk to your doctor about what foods are appropriate). High chairs also may or may not be available. Basically, be flexible. In some ways, babies are very easy to travel with - they tend to just go along and are happy with playing anywhere.
For touring, a stroller is great but not always allowed in sights like museums. Have a sling, ergo, or other front carrier (back carriers are great for hiking but also not allowed in many sights). Elevators aren't always easy to find, so the carrier helps with that, too. Venice is full of stairs on the bridges so a stroller isn't great there.