You need to know the diameter of the shaft. Does the shaft come out the side (normally front or rear) or does it come out the bottom? Get the HP from the Kaw. You'll want that as well so you can try to match.
Also, try to get measurements for the 4 bolts that hold the engine to the frame.
Take some pics of your engine. Make sure things on the replacement match up closely. E.g. the starter, carb... If they're not close, you'll find yourself having to change throttle cables, electrical wires...
If you post a couple pics here of your existing engine, we should be able to confirm your selected replacement engine once you narrow it down to a couple.
What State or Region are you in? If other members are like me, we normally have a spare engine laying around. E.g. I have a 2-cyl 18HP Kohler (Command Pro?) engine that runs perfectly laying around. Craigslist may be another option once you find what you need for an engine. It's not unusual to buy a whole lawn tractor on CL for cheaper than what a new engine costs.