It sounds like the only you thing you can do to make things right is to think about moving closer or in the same town, if the distance is the only problem then thinking about relocating is probably the only solution. The challenges you face as a long distance couples can be harder than people that are in normal relationships where they see each other all of the time, depending on what level the relationship is on. The relationship is new, and has not been given enough time to develop, the challenge to keep it alive is greater than if there has been more time shared. What you are going to have to do now is think positive. Don't look at your relationship as being doomed, because of the distance between you and your girlfriend. Think of an end goal to the separation or possible relocation of either you or your girlfriend. You and your girlfriend should agree on the time frame as to when this arrangement will happen.The deadline should be mutually agreed, because if it's just one partner setting the date, the other partner may feel pressured and may even find the relationship an impediment to personal growth.
Communication is a must more so in a long distance relationship. With internet, reaching out to your partner is no longer impossible. Emails and phone calls are great ways to establish intimacy, and can bridge that distance. Also, take the time to write long loving letters to each other to spice up the romance. Try to plan to meet at least once a week and if that is not possible once a month. This is an important step to keep the relationship alive and if you consider your relationship a priority, you would find ways to meet up, even though it may get expensive sometimes. It adds up to the excitement whenever you and your partner has a date to look forward to, like a shared weekend or even a once a month date. Build up the trust, it's normal to feel fear and anxiety that your partner may become unfaithful because of the fact that you are not together most of the time but in order for the relationship to last then she needs to know a time that the two of you would possibly be together I think that would ease her mind alot.
Then you should give her the time she asked for maybe a week or two to think things through and then contact her after the week or two weeks is up and ask her if she has made up her mind and if she says she needs more time then give her more time she will respect that you are willing to give her time to think about things. All you can do is give her time and hope that she makes the right choice.