MNSmith,
The Suburban cab/body, of course, requires a larger and more complex dolly than would a pickup cab (I have made dollys for both). It is possible to build a frame/dolly made out of 2x4s and 2x6s, as suggested by Ben.
Support the "cab" rear floor in at least 4 places (6 places might be better). I think the Suburban cab is attached/supported by the frame in at least 8 places. If the weight of the cab/body is not supported fairly equally from front to rear, you will most likely break the joints/filler at the upper rear of the side doors, where the front-cab is attached to the rear-body (this joint was covered/filled/finished at the factory with lead).
You may be able to make rigging to lift the cab/body with an engine lift but I suggest that you enlist the assistance of 6 people to lift and move the cab/body from the frame to your dolly. You could shim and adjust the the support points with cedar shakes.
I cannot find all the pictures that we took (I have learned the hard way that you can never take enough pictures) but here is a little look at an early "dolly" that used
6x6s and wheel dollies. The cab was lag bolted to the 6x6 cross-pieces, and it was very easy to roll the cab/body around. Another wood-frame dolly was built but the photos have been lost.
All of this is further complicated if you plan to remove the rear floor and if you want to spray paint the under-body (I brush-coated with rust-converter/encapsulator).
Tim
