i agree with diana, let her continue to visit baby sitter, cats in my opinion are not good to have around unless it's adults or older kids only in the house (strong immune systems), the litter boxes contain a lot of poisions and bacteria that children can inhale and get sick off of.
if you do get her a cat, get a female, my friend had a male, and did not fix him and was very aggressive towards him, always came to work with scratches and even a bite once.
i got my daughter at that age a hamster, and i only made her feed and water her friend, but i changed the cage outside so the bacteria flying around only got to me, and no i wont do that again. i would go for a bunny, outside, up off the ground in a hut so all she will have to worry about is feed and water at her age, and then mommy and daddy can go scoop up the pebbles, and maybe put them in the garden for fertilizer :)