Increasing calories from 1200

Hi,
Since the end of May I've been eating 1200 calories (most days I would have just under that and one month during Ramadan I ate around 900 calories). Recently I've been feeling a little more hungry and from what I read on here, 1200 calories is too low, so I would like to increase my calories to around 1300.

So far I've lost 23 lbs which isn't a huge amount considering how much others on here have lost which makes me worry that if I increase my calories I'll not lose at all. Last month I only lost 3 lbs; I worry that increasing my calories will mean I lose much less than that.

MFP recommends that I eat 1200 calories before exercise.
I calculated my BMR and TDEE which are 1448 (BMR) and 1778 (TDEE). (Calculated using this site: http://scoobysworkshop.com/calorie-calculator/ )
It says I require 1390 calories per day to lose 36 lbs in a year.

Do you think it's worth increasing my calories? I have in the past gained weight on 1600-1800 calories so I know I can't go much over 1200 calories. Has anyone increased their calories from 1200 and still lost weight??