The CL01-12 is a higher-voltage version of the CL01-09, rated for 12kV, while both have the same forward current rating of 350mA.
At a guess this would seem a suitable replacement but with a higher voltage rating.
The one you want to replace is rated at 9kV.
You don't mention why you only want to replace the diode and no other component(s) [magnetron, capacitor, fuse, control module, etc] so I assume those all tested OK and the reason you want to replace the diode is because it tested faulty and the microwave is no longer heating.
(I also assume you know that for reasons of safety the power capacitor has to be suitably discharged before working on the oven)