I have heard it is an insult to God, Himself, to refuse to be a godparent to an individual being baptized into the Orthodox Faith.
You never know....you might be a bigger influence on this child than you think.
Even correspondence is important. You don't have to physically be with her, to influence her.
How much "good" do we reap from reading other's posts on this Web (not even thinking of all the other Orthodox sites on the Web).
I, for one, have learned much about my Faith just from reading other's works.
So, simply by corresponding with her...and showing her you love her...she will be open to what you have to say - by pen if not by word.
It's a great honor and responsibility to be a godparent. I know that I have done many things in this life since becoming a godparent, that I would never have thought I would be capable of doing. You find a strength and a perseverance you didn't know you possessed. God not only helps the child, but, the godparent, as well!
My opinion - go for it! Do even what little you can to help that little girl grow into a good Orthodox woman! Be her example! Let her know you love her....and she will emulate your good deeds!