She made all the effort to make her point and tried to convince you to agree with her. You should have commended her for her good heart and the thoughts she put into the presentation.
Did you read the petition? If it did not advocate violence, you should sign it. That sense of accomplishment is precious for a child.
You do not need to air your disagreement at this moment.
When watching the news together with her, you can say: it is wrong to engage in violence other than self-defence. It is wrong to destroy other people's property. Separate this from her presentation.
Ask her to study the history of blacks in this country, all the way back to the plantation days. Ask her questions about what she learned. You don't need to know the details, have her tell you what she learned.
(Some interesting questions to ask her. What are the Jim Crow Laws? Which political party enacted those laws? Which party did the KKK belong to? Who revived the KKK in the 1910s? Who are the politicians making promises to the black communities and what are their results? ...)