Increase Calorie Intake if Exercising?

Yes. You body needs that minimum to function and it won't be there if you burn it off with exercise. That's one of the reasons I love working out. You get to eat more! I'm at 1200 calories too (my job involves sitting around all day) and it's pretty hard to stay at 1200. So exercise gives you a bit more wiggle room with food and it'll help you body change faster!

You need to understand the method of calorie counting that you are using...there are two typical methods...the NEAT method (Non Exercise Activity Thermogenesis) and TDEE method (Total Daily Energy Expenditure).

MFP is a NEAT method calculator (that includes a weight loss deficit in your calorie goal based on how many Lbs you said you wanted to lose). What this means is that when you set your activity level, you do NOT account for any exercise...just your normal daily hum drum. Conversely, the TDEE method does incorporate your exercise into your activity level. So, with the NEAT method (MFP) exercise is extra activity...because you've gone above and beyond your NEAT and that activity needs to be fueled to avoid having too large a deficit. Netting below 1200 calories really isn't healthy and really should be done unless you're under supervision of medical professionals. Your 1200 calorie goal is for just being alive, going to work, cooking dinner, etc...you normal daily hum drum...you add exercise in there and it needs to be fueled. Also, you don't have to kill yourself with exercise...this is why I always tell people to exercise for fitness...the "burn" is already built into your diet.

Once you understand the methods, you also understand that they work 6 of 1. MFP gives me a NET calorie goal of 1850 calories to lose 1 Lb per week...with exercise I was eating between 2100-2200 gross calories and losing about 1 Lb per week on average (not linear). I switched to the TDEE method and do TDEE - 20% to lose roughly 1 Lb per week...my TDEE is 2,650 calories (to maintain weight with current activity level, including workouts)..TDEE - 20% = 2,120 calories. As you can see, the calorie goal is roughly the same between methods.

You need to understand that there is no reason to create a huge deficit with exercise...it's already built into your calorie goals. This is where everyone seems to get hung up...they think their calorie goal is maintenance or something and they have to create a big gap with **** tons of mindless cardio...you don't have to.

Just make sure you're not overestimating burn. Data base numbers are pretty wildly off...machines are a little better...HRM is even better, but it's all still estimate. My calorie burns I ate back equate to roughly 70% of my burn per my HRM to account for estimation error.

Going to fast and too large a deficit will also cause you to lose a lot of muscle and lean body mass in this process so it isn't advisable. Also, if you search there are numerous threads about people netting 500 calories per day or whatever for prolonged periods of time and losing their hair, losing their periods, etc...it's pretty nasty business when you mall-nourish your body.