I assume that the plate will not fit because the Genesis has a different shape as far as I know. I own a Weber Q-3000 grill and the plate fits perfectly!

I don't think so. The grill grate is too small on the Q1200 a depth of 45 is needed Q1200 only has 32 cm. I run the plate on a Q3000

The plate can also be used on the left :-)

Yes, I run the plate in a Q3000. Fits perfectly.