"but I do not believe the railroad was completed until after the war ended"

The railroad may have not been completed in 1861 when the war broke out but the railroad was at least completed in 1862 all the way to the White River at DeVal's Bluff. The report of the Union ironclad gunboat USS Baron De Kalb (St Louis) in the naval OR's clearly states that on January 14th, 1863 the Union Infantry from transports the De Kalb was leading up the White River, after the fall of Arkansas Post, captured two 8 inch Columbiah guns loaded on railroad flatcars waiting for transport to Little Rock. So there is no doubt that the portion of the railroad from Little Rock to Deval's Bluff was functional.