The Alabama Genealogy website has an Alabama Statehood Map that shows the state's borders and counties as they were when it was first admitted to the Union as a state in 1819. The site OldMapsOnline.org has digital copies of many detailed maps of Alabama, which were made between the years of 1815 and 1825.
The National Archives has a physical copy of a map of Alabama circa 1819. The Office of the Chief of Engineers of the War Department created this map for its own planning purposes. The map includes county names and boundaries as well as towns, trails and roads. It also shows the boundaries of Cherokee and Creek lands and villages. View this map in person by visiting the agency's location in College Park, Maryland.
The Alabama Government Archives has a large collection of maps depicting its state. These maps show the entire state, its counties and its municipalities from various eras. These archives also have maps showing railroads, postal routes and topography, among many other subjects. The maps are not available for online viewing, but you can search the online database and submit a request for the map you need. The agency mails the requested copy for a small fee.