Listen to Alfred, not Bumpy.
The mosquitos and black flies that Minnesota is noted for are largely gone by September, so no worries there.
Itasca State Park is a great place, the Jewel of the MN State Park System. We camp there every year as the closer to our camping season in Late September/early October. Amazing that the mighty Mississippi is just a creek that you can cross in a couple of steps. The Wilderness drive in the park is a great drive and even better with a bike. You'll see the largest Red and White Pines in the state. They have a new Visitor Center with lots of displays, and the Douglas Lodge and restaurant is one of the oldest buildings in the park. Be sure to have a dinner there overlooking Lake Itasca. Lake Ozawindib is a great Bass fishing lake if you are into that. Climb the fire tower along wilderness drive for a great view of the countryside. There are many hiking trails, and a paved bike trail that runs the length of the park.
There are two campgrounds at Itasca SP. If you like wooded sites, then choose pine Ridge campground. The other CG, Bear Paw, puts you closer to Lake Itasca, but it is more open, with few trees.