People don't just lose interest over night without a good reason unless it wasn't really love to begin with. You need to have more confidence in yourself and the relationship. If she walks away that quickly, then you need to know it's her loss. But I doubt she will. It seems the two of you have a good thing going. I doubt she wants to lose it any more than you do.
Worrying won't help anything. Try not to take everything so seriously. Just enjoy yourself. Focus on continuing on getting to know her and making sure she's what you want as well.
Whatever is meant to be, will be. Nobody knows what the long-term future can bring. You just need to do your best to continue building a healthy, loving relationship each day. If she's the right girl for you, it could end up lasting a lifetime. If it doesn't, then it just means you'll have eliminated somebody who was wrong for you and moved a step closer to find the real love of your life. You'll be fine in the end regardless of how it plays out.
“This planet has - or rather had - a problem, which was this: most of the people living on it were unhappy for pretty much of the time. Many solutions were suggested for this problem, but most of these were largely concerned with the movement of small green pieces of paper, which was odd because on the whole it wasn't the small green pieces of paper that were unhappy.” ― Douglas Adams, The Hitchhiker's Guide to the Galaxy