Have you met her in person? That's important, for any relationship.
It's difficult for me to separate my own situation from yours. For me, if she knows she's a girl on the inside... and changed her body on the outside, then she is a woman. Breaking up with someone over simply BEING transgendered is bullshit.
However, there is baggage that goes with dating a trans person. They've usually had a hard time of it, and might suffer from the depression/anxiety of growing up in a hostile culture. Also, a trans girl cannot become pregnant. For some, that's a game changer. I suggest you consider what your expectations from the relationship are, what's absolutely necessary and what isn't, and whether or not you can have that with this relationship.