Update:
I think things turned out pretty well, though there were a lot of unexpected twists.
As it turns out, there was a reason for why meeting her for the first time was nerve-wracking beyond simple scheduling problems, as you surmised. And, as I was starting to suspect, her being trans did factor into it and I should have considered that.We eventually met in a completely different location long after my initial plan fell through, and the initial meeting was really awkward. Turns out she's pre-everything and was afraid of meeting me after I'd been seeing her as female online. Especially difficult was the fact that she'd had to detransition earlier sue to a less-than-ideal living situation. So, she showed up in guy mode in order to let me know the truth. I was honestly quite shocked and things were really tense and uncomfortable at first, but we managed to get over it as we talked for a while and got to know each other better. We eventually managed to bond really well over our shared interest in roleplaying games, and I think it ended really well considering the circumstances.
The advice of "treat her as you would treat any other girl" is a good piece of advice in theory, but in practice I'm learning that being trans can really be important to take into account when considering the situation. Perhaps a better piece of advice would be "don't treat her like a guy, but keep in mind what she's had to deal with and how it might affect things."