We went to Disney for three days last November with our kids who were 5, 3.5, and 6 months old at the time. We cheated, though, we have a timeshare (on non-Disney property) that's about a mile from the park entrance. That saved us a ton of money vs. a hotel on the property, and allowed us to fuel up on breakfast at our timeshare, head over to Disney, and then head back to our timeshare for dinner, so our outlay for food at the park was pretty minimal. Especially with our youngest being so young, that was a long enough day for us. The kids would relax at the timeshare/pool for the rest of the day, and limiting our time at Disney let everyone relax in the evening and recharge.
However, in your situation where you're going down to see Disney exclusively, I think that staying on the property will allow you to enjoy the extended hours, and get the most out of Disney for the money. We drive down to Orlando at least every other year, so we have the luxury of breaking up the Disney experience over a few years.
Even being early November, it was hot - like mid 80s. Couple that with Florida's humidity, and you really need to be prepared with drinks, sunblock, hats, etc. A stroller is a great idea, because even kids who no longer need one will likely need one after walking/standing all day. After being there all day, I could have used a stroller! Make sure you and your family stays hydrated, everyone gets cranky quickly when they're overheated. Plan bathroom breaks accordingly, as well - before you get in line for the ride We also packed some snacks for the kids, as being hungry won't help the situation either.
We had a 3 day unlimited pass for all the parks. We focused on the Magic Kingdom and Animal Kingdom for two of those days, which were great. The third day I took our oldest son to do the Test Track ride at Epcot (which was a disappointment for me, but I might have been expecting too much from the one car-related ride!), and then we went back close to dinnertime as a family for some more rides, the Fantasia show, and the Magic Kingdom fireworks (which were unbelievable).
The most important advice I can give mirrors what I've seen a couple different times in this thread - no matter what you have planned, be responsive to how your child is feeling/doing. Disney is an awesome place, but it's no fun once you've hit the wall. Heading back to the hotel for a quick lunch, power nap, and then heading back to the park can make your day that much better.
FastPass is a life-saver, especially for the more popular rides. The Disney wait time apps were a huge help, as well. We did some planning before the trip for the things we thought the kids would want to see, but we were very flexible. If you're not flexible, Disney will be your worst nightmare.
We had a great time, and it was a good intro to Disney. I know we'll be back!