Hi beeuurkes, welcome to the site.
As for your question, I'm a little torn. Even with the most gentle of children, they can be 'rough' towards animals, when they're trying to pet or pick them up. (Not purposely rough, of course.) Also, if it was my cat in the house with a child that young, there would have to be complete supervision at all times when they were near each other. Not only for the cat's sake (in case the child pets them roughly or picks them up in less than a gentle way. Or pulls his tail.. etc.), but for the child's sake. Cats don't usually just hurt someone for no reason, but I know my cat will at least smack (no claws) me if I annoy him, and he could do the same to any child who just wanted to pet him if he thought he/she was trying to harm him.
I think having a pet as a child is a great thing, I really wish I had one growing up, but I don't think they should really be used as a playmate for a 4 year old. It just seems a little young to me. I'd personally wait til she's a bit older, and fully understands what having a cat is all about.
Maybe check with a local playgroup for children? I don't know if she goes to daycare or not, but that's a great way for kids to interact with each other. Or maybe a teenage cousin could 'babysit' and give the child more playtime that way as well. I know I always enjoyed time with my older cousins growing up.
Anyway, that's just my opinion on it.