Answer:
2nd cousin, once removed.
The key is finding the common ancestor. Your great-grandparents were her great-great-grandparents.
Your father's cousin is your cousin once removed (since these is one generational gap). His/her children are your 2nd cousins (with no 'removed' since they're your generation), and their children are your 2nd cousins once removed.
http://stellar-one.com/genealogy/cousins.htm
As for dating, that's up to you and her, and how you both feel about the closeness of this blood relation. It's perfectly legal, if that's your worry.