You can start to imagine your late cat as a ghost. Say, a kind of spirit animal that will help you in dreams, rather than harming you on some level. A cat could, say, turn into a giant tiger and pounce on any other nightmares that are trying to kill you.

You can affect your dreams on a waking level. I occasionally plan mine out my writing a story that hooks in my current dream themes, and thinking about the story and rereading it, letting it marinate in my head for a few days.