Ferrocement is incredibly strong yet inexpensive and easy to build with. In this doghouse, I know my dog will be safe from hurricanes, tornadoes, earthquakes, and small tonnage nuclear detonations.
Assemble a dense wire mesh in the shape desired. The surface must curve in two planes, as on a sphere or an egg. Flat plane, cylinder, or cone surfaces will not be strong. Use at least 4 layers of hardware cloth and/or chicken wire. The finished wire mesh should be mashed or laced to less than 3/4 inch thick with no holes large enough to stick your little finger through.
Slap on the concrete, working it thoroughly into the wire mesh, removing all voids. Excess concrete will fall through the mesh to the inside. Scoop it up occasionally and use it on the outside again. When the wire mesh is completely filled and covered, smooth the inside and outside surfaces so the concrete layer is less than 1" thick from inside to outside. Apply all the concrete in one session, to avoid a weak seam between old and new applications. Keep the concrete damp for a week by covering it with wet towels and plastic. (28 days for maximum strength).
Now Frisky will be safe and secure. When Armageddon comes, I'm heading for the doghouse!