Should not have an issue getting a site that time of the year. October will be perfect weather 60-70's during the day and 50's at night. Its a neat park with a ton of history. I've never camped here but have visited it numerous times. Oak Mountain SP about and your south on I65 is also a great place to visit. Cheaha Mtn is about 2 hours east off of I20 with great views and hiking.
In Birmingham a great place to visit is the McWane Center. To learn about Birmingham's ore/steel industry visit the Vulcan Park and Sloss Furnace, both are free are and great places to visit.
