I'd suggest having your new frame READY to install Before removing the body from the old (rusty?) frame so you can quickly get it back on a good frame.
If you remove the glass, doors, interior, etc (everything that unbolts), then a good Nomad body is quite rigid. If you leave in the glass, and interior, it's quite another story as those items add a LOT of weight to the assembly. The seats are easy to remove and reinstall, so I'd suggest removing those at the least before the frame swap.
I think if you didn't leave it off a frame for very long, AND supported the body assembly with a beam (landscape timbers are what I've used) under the rockers, and tie across from beam to beam under the body with additional timbers, it would probably be OK in a loaded condition (ie. with glass in place)... just have to take it step by step and be careful...