I purchased a 67 Chev that was imported, converted and sold brand new through a Victorian dealership in 1967. It hadn't been registered since 1980 which pre-dated VicRoads electronic database so there was no record of the car in their system. I didn't have import papers but the car still had the expired 1980 rego sticker on the vent window, however this wasn't good enough for the Department of Transport in SA.
So, with no electronic record or import papers the Department asked that the car be engineered prior to going across their own pit for inspection. Luckily the original 1967 conversion was deemed suitable to both the engineer and the Department and therefore registration was issued.
Long story short. You probably wont need import papers but an engineers report for the vehicle plus the Government inspection across the pits is probably what they'll need. Ask the question first of Motor Reg in your state before buying or spending any money on the car.
Also, keep in mind that it might get expensive if the RHD conversion fails the engineers inspection, I've heard a few horror stories associated with old conversions.
All the best, hope it goes well.