Lulo

Experiencing divorce is really hard on a child, especially her age. They begin to reflect much more then and changes are felt a lot more because a child of nine is just pre-teen and a lot is beginning to happen to her body and spirit.

For her the adult world is incomprehensible and she probably feels very alone. I think it would be a good idea to find a children's support group where she can meet others her own age who are going through similar things.

As her mother you should not try to reason with her, because you can't reason with feelings. Tell her it's okay to feel the way she does and acknowledge her sorrow and anger and frustration.
But you can also tell her that you disagree with her view on love and explain your own thoughts on the subject, not to correct her or rationalize it, but as an exchange of feelings and thoughts.
Talk to her about her doubts and don't try to explain to her that love is not all bad. Right now love is and no words will change that fact.
But you can tell her that you love her and that her father loves her, as a way to express a form of love that is stable and unending.

If you give her space to feel all the conflict emotions she's feeling, she will begin to reflect upon things herself. In time she will realize that not all love is bad, but right now she needs to blame something or someone and love became the target. Eventually this will phase out.