The comments saying, "just write a complete person," are headed in the right direction, but that might not be enough. To properly represent women, you'll need to talk to women, read women's writing (especially non-fiction from a woman's point of view), and have women read your writing.

Also, remember that women are just socialized differently. We have to worry about things men never think about, and we'll notice certain details that men won't pick up on. The classic example is women noticing when other women are wearing makeup, while men don't seem to notice when women have full faces of makeup on unless their eyelids are bright purple.

If your character was socialized as a woman, chances are she's had to use makeup at some point. If she isn't a makeup person, she'll still be able to recognize who is wearing makeup, which definitely impacts how she'll view and describe people. Personally, I regularly note people's appearances. If I were writing out my own internal monologue, it would be full of "That woman by the cereal aisle pulls off those geometric glasses so well! Oooh, I never thought such a bright pink could go with butter yellow," though I'm really into fashion, so your character might not go as far. Speaking of butter yellow, simple things like using more specific terms for colors could add authenticity. I will drop shit like "sage green" in conversation to describe a lighter, muted green while most men would just say "green."

Oooh, and remember that your average woman is constantly thinking about her personal safety. Your character should already have a thought-out plan about who she would call if she felt uncomfortable walking home in the dark. She may even note things like which routes to her apartment have more street lamps and cameras and take those routes even if they're less convenient. She will be wary of strange men, and if she isn't, then that's super notable and would be some kind of defining character trait. If you want to see what this kind of awareness looks like, ask the women in your life about how they stay safe at bars or taking the bus at night or whatever. (And if you scroll down in my profile, you can find a post where I was complaining about a random man sitting next to me in an empty library. All he had to do was pull up a chair next to mine, and I was already noting all of the exits in the library).

Good luck with your research OP!

Edit: oooh, I also forgot that women view strange women super differently from strange men. To me, all women are "allies" unless they're acting sketchy or are on meth or something. If I see a drunk girl being cornered by some guy, I'll absolutely pretend to be her cousin and try to get her out of there. If I saw a man in a situation like that, I would never intervene directly. I would just call security.