I verified that John Cooper Dunn is listed on the Rolls of Co. C not D 7th Miss. He does not, however, show as being mustered. That could mean that he signed up for the "volunteer " company, but did not go when the company moved to the coast.
I found some more on the Dunn;'s of the 7th Miss. We may find that he could have served in another regiment such ass the 33rd since there were Dunn's in the regiment; notably Matthew Dunn who wrote many letters and had close ties to the 7th and many other units in the Amite County area.

There were three Dunn's in Co. C as follows:

Dunn, Dillingham M. pvt. Not mustered

Dunn, E. T. Pvt./Corp. wounded at Munfordville and captured in KY "Slightly wounded in the back of the neck at 9:15 standing in line in open field to the left and about 200 yards from the fort-national archives casualty report.; exchanged; wounded at Atlanta 7.28.1864, lost leg (Ezra Church/Lickskillet Rd.) [See Matt Dunn Letters 33rd Miss.]

Dunn, John C. Not mustered

Thanks for the pass along, George

Ron Skellie