Do you think I should report an ex-friend of mine that's neglecting her child?
How do you know she's neglecting her child?
It's clear that she's not taking care of her and she's a bad mother.
If she really is neglecting her child then you should definitely report her to child services. If this is just to get back at someone that used to be your friend, then you may want to think about your motives.
No, it's to protect her child, but getting her in trouble is a bonus.
It's good to be concerned about the welfare of children and protect them from situations where their care is neglected. Just make sure you're doing this for the right reasons and your allegations are true.