I grew up in that area and spent many days in and around Gettysburg. My boyhood home was along the Appalachian Trail less than a mile from Caledonia State Park.
Caledonia is going to be very peaceful and quiet in October. You're likely to have morning frost late in the month.
But check the camping facilities at Caledonia. There are multiple campgrounds, some of which may be closed at that time of year. Unless they've changed things a lot (and it has been a while) facilities at the Caledonia campgrounds range from dry tent sites at the low end to 30-amp electric only at the high end. No on-site water or sewer hookups. It's about a 20-minute drive to Gettysburg.
As for the battlefield itself, for a non-history buff I agree that a (full) day is probably enough. Don't just drive around with a map. Get either an audio tour or hire a licensed guide. The guides (They used to ride in your car with you. Not sure if that's still the case) are not expensive and are definitely worth it. They really bring the events to life.
See https://gettysburgtourguides.org/reservations/
On a second day, consider spending a couple of hours at the Eisenhower Farm, located by the western edge of the battlefield along Seminary Ridge Road. https://www.nps.gov/eise/index.htm
You're smart to go to Gettysburg in the Fall. Leaves will be turning color and traffic in town will be light, especially on weekdays. But it's a cramped old town with narrow streets most pleasantly negotiated in a car.
Local apples will be in season. Take a loop that runs Northwest from Gettysburg on PA 34 to Biglerville, then Southwest on PA 234 taking a right in Arendtsville to stay with 234 to US 30 and back to Gettysburg. Between Biglerville and US 30, Be sure to stop and get some fresh fruit and maybe a Shoo-fly pie from the farm stands along the road.
For some great views and a pretty country church, about 2.5 miles North of US 30 on 234 turn onto Church Road and drive up the hill to St. Ignatius Loyola Catholic Church. My parents are buried there. Look for the headstone with two hearts. You can drive back down to 234 or follow Church Road to US 30.
If you're a golfer, play a round at the public, state-owned course in Caledonia. The clubhouse is in the campground South of the US30-PA 233 intersection. The fairways are hilly and some are fairly narrow.
Or take a hike along the Appalachian Trail, which passes right through Caledonia Park. Going South from the park is an easy walk. Going North heads straight up the side of a ridge. The park also has several other walking local trails. I recommend Ramble Trail for an easy walk in the woods.
You've picked a great place for a low-key Autumn visit. Enjoy!
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