Even though the Appalachians start up in coastal Canada, for your trip I would focus on the southern part of the range.
A good starting point would be Shenandoah National Park. Skyline Drive, Big Meadows campground, some easy hikes to waterfalls. Bring a kid carrier backpack and you will be in great shape.
Drive south and you can go to Luray Caverns. Definitely a lot for a toddler to see and experience.
From there you can take 81 south or the Blue Ridge Parkway. I'm never patient enough to stay on the Blue Ridge as the speed limit is about 35.
There are some places to take in along the drive but I would head to the Smokey Mountains. National park, Gatlinburg, Dollywood, even over the Asheville NC to the Biltmore Estate. Plenty to do from nature to crowds.
Then you can head to Iowa via St. Louis and stop at the Gateway Arch and continue with a nice ride up the Mississippi River.
Tom and Katharine
'07 Winnebago Tour 40TD, 400hp Cummins
RVing for 19 years & 150,000+ miles