Have a feeling I'll die in my20s...
Then re-phrase it so it doesn't sound "weird." Say something like this, "We've been talking over messages for a while, and I'd like to try video chatting sometime if you're interested..." It probably would weird her out if she hadn't really got to know you. At least for me, if a guy I barely chatted with asks me to video chat, I wouldn't be down.
edit: Saw first post, and noticed you've only been chatting for a few days. Wait it out a little longer to video chat. But video chat before you meet up in person.