To find the part number for the gasket I need the full string of numbers stamped on the cooling air cowl of your engine, right above the muffler. The Model is 80202, but I need the Type to identify which variant it is. The third group of numbers, the Code, will tell us the engine's year, month and day of manufacture.
The gasket's name is Crankcase Gasket. The standard (i.e. 0.015" thickness version) gasket for a generic 80202 is Part Number 270833. There are two thinner versions available, to adjust crankshaft endfloat, but you probably will not be able to buy them in Australia. The correct procedure is to fit a standard gasket and measure the end float with a dial gauge, then either fit a thinner gasket, or add a thin one to the standard one, to achieve the required endfloat of 0.004 - 0.008". However I doubt you have a dial gauge, so for this purpose I suggest you assemble the engine with a standard gasket and feel whether there is endfloat but not much of it, and the crankshaft rotates freely with the spark plug removed from the engine. If so, it will be fine. Incidentally I think you will probably find the resistance to pulling the starter when the piston is close to the top of its stroke will not exist when the spark plug is removed. It is a very bad idea to pull the starter with the spark plug installed and without the crankcase cover installed, since a substantial vertical force is applied by the compression, and the crankshaft is not supported to resist it.