She just might have that kind of personality - all kids are different, even siblings in the same house with the same parents. I remember being 5 and 6 and visiting my grandmother's house for the weekend and sobbing my eyes out when it was time to leave. I cried when I was 10 and saw "E.T." for the first time in the movie theater. Being sensitive and being compassionate and having empathy for other living things shouldn't be a bad thing, although I can see where it can be rather trying at times. My daughter just turned 4 and we've been on a number of trips and family vacations in the past year. She always gets sad about leaving our house because she is going to miss our dogs and cats and wonders if they will be okay. Then she gets sad about going home because she's had so much fun on the trip. On the most recent trip we took, she was sad about the trip being over before we had even left. She gets attached to every hotel room we've ever stayed in and even got attached to a rental car we had and cried because she was going to miss it. I think she just associates these things with the fun of traveling and the experiences we had and gets very sentimental. She also is very sensitive to my moods and if I say anything to her where I sound even the least bit negative (irritated, etc.) she thinks I am mad at her. She is just a gentle sensitive soul and I am sure that as she gets older she won't be quite as dramatic about everything, but for the time being I try to acknowledge her feelings as much as possible and not dismiss them.
My mom was huge on being one of those super-sensitive emotional types. One time we went to a movie together and one of the previews for another movie coming out got her crying.