I think it is possible for you to love her, but you are too young for it to be a forever thing. Think of it as a kind of practice love and enjoy it. But be prepared your feelings for her will probably wane.
But don't worry, you will find a new one. Enjoy it, it is probably one of the pleasant times in life, falling in love over and over.
Every person is born unique and have a certain level of maturity. Some people are mature enough to fall in love even at such a young age. I think yes, it's possible to be in love at the tender age of 13. While others never know the feeling until they reach their 20's. The best person who can answer your question is you. Because you know your feelings more than any other person does.