Dont alienate / confuse her with words like ideology etc. I don't think you can do it all in one go, it has to be pockets of info.
Focus on basics she should already know from science; male and female, chromosomes etc. I do think learning about human reproduction and genes and then evolution etc at the science museum in the 80's had a massive impact on my understanding.
Talk about stereotypes; how women and men can do the same jobs. How men and women can wear and like the same stuff. Give examples. But then differences in biology when it comes to child birth, women who have children take time to do this, breastfeeding etc. (That's not really discussed at school.)
Talk about same sex attraction and relationships. In reality, anyone can fall in love with anyone or no one. All the labelling stuff is just a trend.
Referring to stereotypes, you can talk about women who fought to vote, have their own bank account. Get careers. Books on historical women etc.
You could discuss sport definitely. Why are there separate categories?
There's lots of stuff at the moment about how men and women react differently to Coronavirus, due to genes. Women have 1000's of extra genes.
But the basics lie in biology.