Firstly, I'm very sorry for your loss of Carson. I also lost my buddy in March and it still hurts like it happened yesterday.
About a month after my loss, it was so depressing how quiet the house was. I thought there are millions of cats out there in shelters who need good homes, and I still have the capacity to provide one and there might as well be something good that comes from an otherwise horrible thing, so I adopted another cat from the local shelter. She had been brought in by animal protection officers and was obviously in need of a better place.
I'd like to say everything is all good, but I am still grieving for my lost buddy and there are days I know I am not showering my new cat with love like should happen when anyone brings home a new forever pet. I came home one day particularly depressed (something that is always depressing now that my best friend is not in the window waiting for treats) and I called her replacement cat. Then I immediately thought to myself that was a ****** thing to say!
She is a very sweet cat and has adapted well. I know she is coming from a bad experience too, and she is doing better than I am. Not saying this to discourage anyone from finding a new friend after a tragic loss, but it should not be a rushed decision either.
The new cat is slowly finding a place in my heart, but the hole left by the one past is still so big, it's gonna take some time. Wishing you and Kojo all the best.