The way MFP is set up you should always eat back your exercise calories. 1200 calories isn't a lot for someone as tall as you!! I've lost all my weight eating between 1600-1800 NET calories, so days I exercise I'd eat over 2000 no problem!
Also you probably set up MFP to lose 2 pounds a week which is why it gave you 1200 calories only. Losing 2 pounds a week isn't really safe for someone who's got such little to lose. It's only recommended for those who are really overweight and obese. I'm a teacher so I'm on my feet for quite a bit of the day so my maintenance calories is around 2100. If I eat more than that I'll gain, less I'll lose. I highly doubt you'll gain eating more than 1200!!
Check out this website, http://scoobysworkshop.com/calorie-calculator/
it's a great calculator to determine what your TDEE (maintenance) calories are.
I will put it out there, if you've eaten a low calorie diet for a long time your TDEE will most likely be lower than what it recommends. That along with the fact I love food is why I'd never eat 1200 calories a day!