Margaret, many people will simply caulk this gap, but you are right in asking about this; the toilet needs solid support all along the base, not just at shim points.
Here's a method which may work for you:
Take a sheet of lightweight plastic drape (painter's draping or visqueen), and position it over the large gap- half up the toilet base, half out onto the floor.
Mix some fairly stiff plaster, and begin working it in under the wide gap, on the plastic. (The plaster going in under the toilet is in effect wrapped in the plastic; plastic is simply to prevent the plaster from bonding to the toilet and the floor) As it starts to set up, shave the outer edge smooth, either flush to the side of the toilet base or slightly under.
Once it has cured, carefully trim away the excess platic with a utility knife, then surface the plaster fill with a light coating of clear caulking(assuming the toilet is white), and a bead of caulking completely around the base at the floorline. The thin coating of clear on the plaster will help it to blend in with the china finish of the toilet, and keep it from absorbing moisture and discoloring.