The 19th Arkansas was sent to Clarendon Ark in September 1862 and then moved to Arkansas Post where they assisted in the Construction of Fort Hindman and were the Forts garrison. Sickness was still a problem including Col Dawson and many of the men were absent sick at the Sulphur Spring Hospital when the Battle of Arkansas Post happened and excaped being captured and sent north to prison Camps. The surviving men of the 19th Arkansas were organized in Feb. '63 at Sulphur Springs along with the men of the 24th Arkansas and Crawfords Battalion who also excaped capture at Arkansas Post for one reason or another into a "Holding Regiment" designed as the 19th/24th Arkansas Infantry under the Command of Col Dawson. The second in command of this regiment was Lt. Col. Hardy. While designed as The 19th/24th Arkansas Infantry it became more commonly known as "Hardy's Regiment" when Col Dawson resigned his commission due to ill health in April, 1863.
As I said the regiment had originally been intended as a "holding regiment" until the men who had been capturred from the regiments at Arkansas Post were released from prison and exchanged as was the custom of the day. However those men in the prison were exchanged in April, 1863, but they were exchanged at City Point, Virginia by the Union Army instead of Vicksburg by the request of General Grant. They served the remained of the war East of the Mississippi River.
Up until May of '63 Dawson's/Hardy's 19th/24th Arkansas Infantry had remained unattached at Camp White Sulphur Springs. Once it became appearent that these regiments were not going to be reconstituted with the exchanged prisoner, by the time Hardy's regiment was assigned to Brig Gen Daniel Frost Missouri Brigade then at Fort Pleasent on the Arkansas River at Pine Bluff. This did not seem to set well with the Arkansas boys to be attached to a "foriegn" Brigade of Missourians.
In July 1863, Fort Pleasent was ordered abandoned and Gen Frost was to move his Brigade and Hardy's Regiment to Little Rock to be a part of that defence. Here is where Oliver Davis was reported as being A.W.O.L. The muster roll which would have showen him as AWOL would have been taken by his 1st Sgt on August 31st, '63, just a few days before the Battle of Little Rock and the confusion which followed the Confederates retreat from Little Rock.
As Bryan H. has pointed out Oliver's absence could have been for any number of reasons including illness or being on a special duty assignment that the 1st Sgt was not fully aware of. It is most likely that Oliver became seperated from his regiment during that retreat.
As for him joining the Cavalry there are also many reasons for that. First of all men of those time had rather ride a horse that walk. But just as equal a reason was the Hardy's regiment for those who had excaped capture at Arkansas Post had not been involved in any fighting. The cavalry while of little use in grand battles were constantly involved in patroling and skirmishing with the enemy and countering the Union Cavalry patrols trying to probe the Confederates. So it could have been that he just wanted to get into the fight even without proper authority once he found himself seperate from his regiment.
Hope this gives you some insight.