Comes down to this. Are YOU comfortable doing it? If so, go for it. If not, don't. I've done some crazy things before, but they were things that I was comfortable doing. It's your safety, it's your money, it's your life. You decide.
I know that isn't what you wanted to hear. But there's and old saying that "those that are looking for advice are really looking for accomplices"
In this case, I can say that that doesn't sound normal for a girl you've never met. But, again, as others have stated, it's not abnormal either. (Boy I miss the NH's!!) I've had a few others do similar things. But again, it comes down to the fact that it's your decision to make and our experiences may not reflect the situation you're in. We don't know the lady. We don't know if she's trustworthy or whacked out or a set up or whatever. For that you need to use your inner radar to tell you if it smells fishy.
And, since you asked in the first place, my guess is you do.