Not being a DMV clerk in Arkansas, I think all you need is an avadavat of modification. Signed only by the owner, if it was a wrecked trailer it would also be signed by the mechanic or facility that fixed it stating it is back to factory condition.
The differences between modification and rebuilding a wrecked trailer are substantaly different. Each state has its own laws and requirements specific to its own state statues. It is not a big deal to add an axel. Depending on the type, in this case a bumper pull trailer and set-up (deck over or low profile)the additional axel install can be very easy with no modifications at all to the trailer other than attachment of the axel. In other setups, fender removal and tandem axel relocation may be required to ensure proper load distribution. However, in this case I would not now rate the trailer as a 10,000lb trailer because it had an additional axel added. Depending on manufacture, the only difference in 7000lb and 10000lb trailers are the axels.
Not seeing the trailer or knowing the frame set up I would still consider it a 7000lb trailer that better distributes the 6000lb tractor and is easier for the ½ ton pickup to haul. I also think that when GM switched to the new frame in 1998 or 1999 it increased the towing capacity from 7300lb up to 10,400lb; I would check your door or the owner’s manual.