I have been in a long distance relationship for 2 and half years, and we are still going strong... as far as im concerned. If its worth it for both of you, then yes it will without a doubt work. Its fucking hard, and it takes a lot... but like I said, if its worth it, then you work around those things. One of the best things about long distance, even though it gets tiring after a while is that, everytime you guys do get to be together, its like a honeymoon.
If you really want to be with this girl, and you think its worth while even though you two are apart, then go for it. If you don't... you might regret it for the rest of your life.