M.P.
This is tough - I think it is important to say that the kitty got very sick, very fast. And that sickness caused kitty to die :-(
Look online (you tube) for Mr. Rogers - Death of a Goldfish episode. It is phenomenal! You can watch it yourself for tips on how to talk to her about death, or you can have her watch it with you.
She will have questions. I would explain to her that sometimes she gets sick and mommy (other family members) get sick or don't feel good. But that this is different. Kitty was VERY sick and even though she was going to go to the dr, it wasn't fast enough and the sickness made Kitty's body stop working. Reassure her that it is VERY sad when something like that happens. Tell her simply what you told us - that you were taking care of her, trying to help Kitty get better, but "it wasn't enough". Sometimes these things happen :-(
Good luck - I am so sorry for your loss and having to have this tough conversation again, so soon :-(