Some time ago we had a discussion about the evolution of companies that were merged into Hawthorn's regiment after the battle at Prairie Grove.

Based on this information, Hailey's company may never have been at Camp Nelson while it was in use, but rather serving in Carroll's NW Arkansas district bfore joining Hindman's 1st Corps.

It appears from available records and from that discussion that Hailey's company was one of those that had originally served in Gipson's mounted battalion, only to be dismounted and transferred to Hawthorn's/Chew's infantry battalion, which was subsequently merged into Hawthorn's regiment as mentioned above.

Notes from the previous discussion include:

Were Serving in Carroll’s NW Dist in units that dissolved & merged into Hawthorne’s regt
8/29 Hailey’s Co served as cavalry until dismtd 8/29 [but see also 9/16 next]
9/16 Perkins Co & Tomlinson’s Co served as cavalry until dismtd 9/16 by order of Col Carroll

10/19 Fayetteville, Hdqrs. Dist of Ark #18
...
Col A T Hawthorne is assigned to the command of the Bn composed of companies of Dawson’s, Tumlinson’s, Perkins and Hay...est Co’s of [of Brooks brigade]
Brooks’ regt Ark vol, Adams’ regt Ark vol, Hawthorn’s Bn Ark vol and the Mo troops commanded by Lt Col Caldwell will for the present constitute a brigade under command of Col Brooks.
...

10/19 Brooks brigade [including Hawthorn's ] later Chew's] Bn referenced at Camp Reagan
10/28 Brooks brigade [including Hawthorn's ] later Chew's] Bn referenced at Camp Hindman

From "Record of Events" remarks from (new) Co. H & (new) Co. K, 39th Ark Inf-These were Perkins'/Hailey's consolidated Company and Tumlinson's Company, respectively:
Co H-This Company is composed of two Companies---one formerly commanded by Capt Perkins, the other by Capt Hailey-and consolidated into one by order of Hindman. They were originally mustered into service as Cavalry and served as such as follows---Hailey’s Company 8/24 & Perkins’ Company to 9/16, and are paid as such on this roll. This Company was in the battle of Prairie Grove & had 10 men killed and wounded.
Co K-This Company was organized on 7/4 in Waldron, Scott County & marched thence to Big Creek, Sebastian County, to Fort Smith and mustered into service on 7/20 as a Cavalry Company and served as such until 9/16 when it was dismounted by order of Col Carroll.. Served as such one month & twenty seven days when it was dismounted by order of Col Carroll.

12/16 Hawthorn's regiment was reorganized by consolidation of original companies & addition of dismtd companies of Hailey’s, Perkins, Tomlinson

12/16 Perkins & Hailey’s companies consolidated this date [previously served in Gipson’s Bn Ark Mtd Rifles]