Speaking from my own experience I found 1200 calories too limited for a daily basis. It's hard to get in all the healthy foods you should eat plus a little snack that you might want too. I found that I can do about 1400 calories a day and still lose weight. I also find that getting enough sleep helps with the water weight loss. (Although it's only water weight and not fat it's still annoying to see the scale move upwards when you're trying to go the other way
There's also a hormone called leptin that plays a part in appetite control and without enough sleep your body doesn't seem to have enough leptin so you tend to eat more. You want to drink enough water too to flush all the metabolic wastes from your system. I also generally walk 5 or 6 days weather permitting or go to the gym for cardio in bad weather. At the gym I generally do about 45 min of cardio and try to stay mostly in the fat burning zone rather than really push it for the endurance cardio. I alternate between the treadmill and elliptical for variety and I think the body likes to get a variety of different types of cardio activity when it can. I do weight training 4 days alternating upper and lower but I am a definite beginner in that. With what I do, I find I don't really have a steady weight loss each week. Some weeks I might lose 3 pounds, some weeks 1.pound and sometimes I may be neutral or even gain half a pound however when it all averages out it turns out to be about 6-8 pounds a month.
I would suggest you experiment a little, go slow and add 300 calories to your diet and do a min of 45 min cardio and see how that works. Look at your diet and see if you want to change the timing of meals, eat bigger meals earlier, eat less at night, eat more frequent smaller meals or eat less of certain foods you currently eat. See what works for you. Most of all weight loss takes a lot of patience, it seems like forever somtimes but hopefully all the effort will be worth it. Good luck