I had been cutting calories to lose fat but...?

My weight didn't even budge. I realize that it is because I am so close to my natural weight (just wanted to trim a few pounds of fat). I am 5'3" and weigh 121.5. I read that to lose weight in a healthy way I would have to consume about 1300 calories a day as opposed to about 1800 calories a day to maintain my current weight. I eight healthy foods and I jog for a half hour 6 days a week and do a little bit of weight and resistance every other day. Could it be that I need to eat more to lose the fat? I know that if the body does not consume enough calories it's metabolic rate slows. I've been doing this for about 3 months now. I will admit I do slip up on the 1300 calories sometimes but not by much and not too often. I plan on gaining muscle once I reach my goal of losing about 5 pounds. I don't think I'm fat, there are just some things I would like to fix such as a flatter stomach and firmer rear end and inner thighs. Any tips or insight?