How is it that people expect a short person to follow the same diet as person of average height to lose weight

I'm 4'8" and I find it hard to stick to a diet because I'll lose a couple pounds then hit a never ending plateau. I believe it's because of my height. If I'm as tall as a 9 year old, shouldn't I need to consume what a 9 year old would to maintain my weight. Are there any diet and fitness plans designed for the smaller body frame?