Reddit reviews The Day Tiger Rose Said Goodbye

There have been some good posts on this topic over at /r/parenting - you might check out this one, this one, or this one. One bit of advice that I've read several places is to avoid using the phrase "put to sleep", because you don't want your daughter to associate sleep with death - it may sound blunt, but telling her directly that the cat died will be less confusing than the various euphemisms we tend to use. Explain that when animals get old (and people too, if she asks) their bodies don't work so well, and eventually stop working. When an animal's body stops working completely, it means they have died, and they can't run or play or eat or sleep or do anything anymore.

You might think about getting an age-appropriate book about the death of a pet to read with her, such as Goodbye Mousie or The Goodbye Book; two good ones about cats specifically are The Tenth Good Thing About Barney and The Day Tiger Rose Said Goodbye. There's also a more factual (rather than story) book written by Mr. Rogers called When A Pet Dies which might help you answer some of her questions, and the book Lifetimes provides a lovely explanation of death in general as part of the natural cycle of life.