Bit of a tangent, but it continues to amaze how relevant Tolkien continues to be to this day considering he started developing his legendarium almost a century ago now. Gender issues, sexism, addiction, free will, the allure of power and wealth, all explored in an amazingly prescient way that still stands up to scrutiny today.
Although diving deeper into the legendarium, there is the fact that the southrons and easterlings were corrupted by Sauron to worship him as a god. So you could choose to view those descriptions as consequences of that rather than perceived racial or cultural inferiority. And indeed the "fair and beautiful" Numenoreans were at one point corrupted by Sauron in very much the same way.
But yeah, you definitely have to give Tolkien a lot of help on this one, and it's not terribly helpful in the context of reading to your children :/
I wouldn't be surprised though because this does seem to be the modern leftist agenda, to turn every brown person into a victim incapable of helping themselves.
Maybe explain to your daughter it's based on Nordic mythology and turn it into a positive history lesson. OH! And you could tell her that her skin color really isn't the most important thing about her. Just a thought.