You are extremely thin for your height and while I can totally understand that an upward movement of the scale is not what you want to see, does 5 or 6lbs really make that much of a difference? It's not worth obsessing over and once you start you can get into an eating disorder mentality. I've seen people at 5'2" and 120lbs that are rock solid (muscle) and tiny. Maybe your body is just adjusting? Sometimes when you play with your calories or change up your workouts you retain fluid which will eventually go away. Just drink lots of water
You definitely need to eat more. And your weight might go up a bit at first. It's probably water. What you could try and do would be to increase your calories gradually. Going from 1000 or 1200 to 1800 or 2000 calories is pretty dramatic. But what if you upped your calories by 100 every few weeks or even every month. So eat 1200 for a month, then eat 1300 for a month, then 1400... until you're at a good place for your weight, height and age.

. Your AMR (active metabolic rate) will give you an idea of what you need to eat to maintain your weight if you just live your life and don't incorporate any exercise into it. If you exercise you would add in those calories as well.
You very well could just be a naturally thin person whose body is comfortable at a low weight for your height. As long as you are eating healthy I would let your body do what it is going to do and see where it's happiest.
And if abs are your main concern then you should be focusing on 1) body fat % and 2) what you're eating. High sodium foods are going to cause you to retain water (so think anything that's overly processed) and not working could mean that despite the fact that you are thin, your body fat percentage isn't ideal. Incorporating some weight training or resistance training into your days could have a big impact on how your body looks.
But I seriously would not even think about losing weight right now. Get your calories to a good, stable place, add in some exercise and make sure you're eating minimally processed foods. Good luck
