First and foremost, open, honest communication is always the top priority if you're trying to support someone through any complicated thing. Check in with her regularly to make sure she feels supported rather than pressured.
Also, I think framing things as suggestions is probably the root of the concern here. I would back off of that.
Learning and sharing what you've learned can be helpful. Suggesting a course of action, especially if you have not been asked to make a suggestion, can undermine her autonomy.
The primary way trans people are attacked as they transition is having their autonomy questioned, undermined, and rejected. Usually this is from people who oppose their transition, but it is also entirely possible to encroach on her autonomy by telling her how you think she should transition.
I like how he can't even express an intent to protect women without undermining our consent.