As a researcher of The Army of the West, I offer the following timeline for McRae's Arkansas regiment:

March 17 Organization of Price’s 1st Division announced
Little 1st Brigade of Price’s 1st Division
21st Ark Col McRae
1st Mo
2nd Mo
3rd Mo
Gates' Cav
Wade btry

3/20 -S.O. #86 HQ MSG, Camp Ben McCulloch
The following changes are made temporarily in the organization of the Bgdes of the 1st Div of the West, viz:
-Hill’s regiment is assigned to the 1st Bgde, Col Little cdg;
-Rector’s regiment is assigned to the 2d Bgde, Col McNair cdg.
They will at once report accordingly

3/24 McRae’s Ark regt left Van Buren for Des Arc-Memphis-Corinth and on to Rienzi station
3/24 McCown’s Bn joined the1st brigade as the army commenced the march to eastern Arkansas, and ultimately to Corinth, Ms

4/11 --16th Ark lands at Memphis 12 last night & arrive Corinth late in [next] evening. Took RR to camp at Rienzi which was named after Churchill Clark
4/11-16th Ark leaves for Corinth arriving that same night as part of Little’s Mo bgde, but did not leaving the train until afternoon of 4/12

April 12, 1862
Col. McRae,
As you are senior Col. of the brigade you will report to Gen. Beauregard on arriving at Corinth & take command of the regiments and battery there. We will go up with McCown’s Regt. this evening. Please state this to Gen. Beauregard.
Respectfully,
W.C. Schaumburg
AAG

4/14 S O#24, Army of the Ms-III So much of paragraph I, Special Orders, No. 20, from these hqs, dated April 12, 1862, as refers to Johnson's Bgde, First Army Corps, is rescinded, and a division, to be composed of Little's and Maxey's Bgdes, will occupy Bethel, with an outpost at Purdy; the whole under Gen Little. This division for the present will be attached to the First Army Corps.

4/16 Memphis-Price cdg 1st div A of W-asking Beauregard that Little's Bgde now at or near Corinth be returned to him here-due to his attachment to them being from Mo, etc. If needed, I can send other troops recently assigned to my command

4/16 -Camp Rives, Rienzi, Ms-HQ 1st Bgde 1st Div A of W—submitting list of officers who have resigned.
Signed Little, Gen
Incl offices from:
16th Ark
1st Mo 1st Bgde
Lamar Tx Cav
2d Mo
McRae’s Ark

4/22 Camp Rives, Rienzi, Ms-HQ 1st Bgde 1st Div A of W--B Gen Little reporting desertion charges & asking for court martial to be formed of officers of following Regts;
1st Mo
2d Mo
3d Mo
16th Ark
McRae’s Ark
36th Ms Witherspoon

April 29
[2d] Maury Bgde of Jones’ 2nd Division
Moore reg Tx Inf
Garland reg Tx Inf
21stMcRae reg Ak Inf
_Tx reg DC
Adams’ Ak Bn Inf
Bty

May 4
Moore's Bgde of Jones’ Division
Moore Tx
Garland Tx
McRae Ak
Embry Tx DC
Adams Ak

May 8
–21st Ark [formerly McRae’s 15th Ark] was reorganized for the war & Lt Col Hobbs succeeded McRae as Col.

It appears that Schaumburg is referring to Col McRae as the senior Colonel of Little's brigade during the brief period that Little was acting as a division commander under Beauregard. By April 29th, McRae's regiment had been assigned to Maury's [Moore's] brigade.