Austin's Battery definitely disbanded on 23 July 1862. The link below shows that the guns of the battery and all equipment were transferred by Austin to Darden's Jefferson Mississippi Battery. No mention of the men though...
It is interesting to note, however, that in CSR Arkansas Miscellaneous, Lieutenants Hartwell Boswell, James G. McDonald and R. A. Mills of Austin's Battery also have a reference to Trigg's Battery in their records.