Like everyone else said, I doubt it's something to worry about. I'm 5'9"-10" or so, and 130lbs... and I'm only that heavy because of muscle. It's basically all lean and long, since I'm constantly stretching and active and what not, but still... when I was your age, about 5 years ago, I was the same height as now and 115-120 lbs, and it was good for me. Sure, you'll hear the "put on some meat" and anorexia comments, but as long as you're not having any health problems and eating right, it's all good.
The thing to keep in mind about BMIs is that they're really general. It doesn't take into consideration whether you have a small or large frame, or differentiate between adipose tissue and lean muscle mass.
Also, do keep in mind that when you start HRT (assuming you're planning on it, based on how you worded it), typically a m2f will experience redistribution of body fat and a slowed metabolism, among other things, so that may let you put on some weight more easily.
When I let go of what I am, I become what I might be.