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.