Will this diet work for the long term?

I'm 23 years old, 5"2, 130lbs. I want to lose 15 lbs minimum, but ideally around 20. I work out 3-4xs a week, mixing cardio with strength training. Because I have not had any success in weight loss or even toning, I started a food journal recording everything I eat, including how many calories, fat, carbs, and sugar. I'm eating roughly 1300 calories a day with my major nutrition sources being veggies and protein (only whole grain type carbs). I am also taking a weight loss supplement called Natural Fat Burner (3-4 times a day). I only drink water.

I definitely am eating better than before, but I still feel hungry all the time. I will eat a meal, feel full, then get the rumblies less than an hour later. I don't feel like I can increase my calorie intake because then I would be back to where I was before the diet and not lose any weight. I'm able to ignore and push through any cravings, but I'm worried about eventually getting frustrated and binging, or dropping the diet all together. Will my body adapt to this and I just need to give it more time? Or is there any other suggestions?
Will this diet work for the long term?
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