My daughter is about to turn 11, and I have similar hopes for her. Each of the paragraphs below is a category that her father and I have found to be influences on her in some way, and ways we try to approach them.

Provide positive examples. This needs to be both men and women, of course: women who embody the values and confidence you hope for her to have, and men who support, value, and respect the women in their life. The most present and influential examples are her parents (and you seem to have that covered), but also consider the effect of family, (your) friends, community leaders, etc. (Also teachers, which you may think irrelevant in homeschooling -- however, if you ever enroll her in any activities like sports, gymnastics, computer programming, whatever, that extracurricular would still be taught or led by someone.) Be forthright and honest with these adults in your life about the values you hope to encourage in your child, and seek their help and support while cultivating those ideals.

Positive examples can also be found outside acquaintances: female politicians, scientists, engineers, etc. who are (or were, history is important!) trailblazers and leaders, demonstrating

Socialization. Every child needs to have friends their age. These peers (both boys and girls) are met in a variety of settings: play groups (from baby on up), organized activities (sports, dance, book club), community organizations (church, volunteer group), or school. This is the factor that you, as a parent, have the least control over. You can dictate which activities she is involved in (for example, opt for homeschooling), but there's still a practical limit to just how much the pool of potential friends can be narrowed down, and which children from that group your daughter may like best.

Those kids, whether best friends or just acquaintances, will be raised differently, some may be bullies, some may be sexist -- even ones who are raised "right" (by your standards) have the potential to be rude, cranky little brats now and then. It happens, they're kids. The key is how you encourage her to engage with their perspectives, having conversations about their attitudes (particularly negative ones) and ideas.

The hardest part of a daughter's social influences, and I think moreso in your scenario, is how to deal with a friend who has [something] when your child/family does not. In my daughter's case, despite a curated set of movies, TV shows, and other media (which she authentically enjoys while we're watching together), she still mopes that she can't watch whatever latest tween-targeted drivel that all her friends are giggling about at school. This leads me to...

Entertainment and instructional media. There is actually a lot that can be gained from media, even when the media itself contains bad messages. The obvious "good" media would be science shows, news coverage of positive role models, shows or movies with strong female characters -- these can be vetted similar to books. One of my daughter's favorite YouTube videos is Sesame Street's "Women Can". I think that regardless of the "quality" of the content, however, a more important factor is being aware of what is consumed (reading or watching alongside is excellent) and being ready to have discussions.

Awareness. I feel that knowledge of current events and society is important for her to develop as she grows up. Otherwise, once she hits 18 and goes to college, she'll be completely unprepared for the world she encounters. The first time you're told "you can't do [thing], you're a girl", it's a surprising and unpleasant feeling. I think that being able to bounce back from that requires self-confidence, but it also helps to have some practice, as well as understanding where that objection might be coming from (fear, misunderstanding, ignorance, stupidity) -- so you can engage with it in an appropriate manner.

Engagement. The goal of this is eventually that she'll be confident and saavy enough to engage with discrimination she'll encounter as an adult, but the groundwork has to be laid earlier. Let's say I restrict a certain source of information ("you can't watch Latest Tween-Targeted Drivel") -- she will want to know why. And that leads to subsequent, harder questions. A TV show can't just make me feel bad about myself. Friend watches it all the time! If it's so bad, why would it be on TV? These are all good questions to ask, and can lead to thoughtful, empowering discussions. Even great literature, even the classics, has plenty of tricky or questionable content that should be explored, criticized, and questioned. Rather than avoiding media altogether, I'm instead trying to cultivate critical consumption. When she sees something that conveys a biased or bigoted perspective, I want her to think about why that isn't accurate, what exactly they're getting wrong, ways it could potentially be fixed (could the casting be changed? could the plot or character be developed differently?), and so on. When she's reading a book or watching tween-targeted drivel at a friend's house, she has a foundation of self-confidence and social justice that she can use to actively engage with negative messages, whether subtle or obvious.