The only information on their arrival that I've found is that found in their individual CSRs.

George Carr, Private, Company F, 1st Regiment Alabama Infantry, enlisted in Alabama, captured at Island No. 10 April 7, 1862, arrived at Camp Randall, Madison, Wis. prison camp, guarded by 19th Wisconsin Volunteers, died April 22/28, 1862, his mother Lueretia Carr filed claim for the settlement of his accounts Nov. 18, 1862, no other records

M311: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Alabama

Sampling of the deaths in Camp Randall

28th Geo. Carr Co. F 1st Alabama
http://civilwartangents.blogspot.com/2011/04/confederate-prisoners-at-camp-randall.html