No, a 2005 Chevrolet Cobalt with an automatic transmission should
not be dolly towed. Towing a vehicle with an automatic transmission on a dolly puts stress on the transmission because the drive wheels are still turning. This can cause significant damage, potentially rendering the transmission unusable.
To tow a 2005 Chevrolet Cobalt with an automatic transmission, you need to use a flatbed tow truck or a vehicle with a tow bar that properly disables the drivetrain.