RPM, see if you can, rent a full size window van, with a trailer hitch. Rent a towbar that clamps onto the bumper, tell U-Haul you're towing an old 60's car with a solidly attached front bumper "pre-1973".
Just make sure you disconnect the rear drive shaft on the Chevy, (unless it's a stick shift).
I'm afraid your Toyota may be too light weight to do the job. As BigPappa mentioned, if the front suspension is pretty loose, you could wind up doing the "shimmy."