I think if it were just up to me it would be a long time before adopting another cat. But the other cat is still with me, and so I will be waiting to see how she feels in a few months and what she might want. When he first went into the hospital, she looked for him every day and kept meowing at me to produce him for her. But now she seems to understand the situation, however, and that is a relief.
We all deal differently with grief... you don't need to do anything if you're not ready. But I was highlighting an option for you.
In the past I never replaced a pet with another... but I was younger then. Now as I'm getting older, and maybe due to the fact that I live alone, I feel that if I were in your shoes in my own circumstances, I'd buy/adopt another pet. Be it a cat, dog, parrot... etc. I believe an animal lover is an animal lover for life.
Stay blessed dear...