Am I eating enough calories?

That kind of depends. My nutrition textbook recommends eating 500 less calories than you use each day. Your weight, height, age, and metabolism are used to calculate that, along with any exercise that you do. As far as I can tell, the calculator for this site is accurate- so if you put in all your stats and tell them you don't want to lose any weight, that's how many calories you use a day. It's possible if you're short, thin, and spend most of the day sitting that you do only burn 1700 calories a day, but it's unlikely.

1200 calories is the absolute very least you should be eating, and is actually considered by my textbook to be a starvation diet. You have to be really careful with a diet that meager, especially if you aren't getting enough carbs, because your body might start producing ketones, which can build up inside your body and kill you. Your body might also start eating your lean muscle mass. As you probably know, muscle mass burns calories just by existing, so you really want muscles if you're trying to lose weight.

Also, remember to put your health first. Losing weight quickly often fails to address the underlying cause of the problem, and often results in gaining it right back again. You might think to yourself "that's no big deal, I can just lose it again." There are many studies that show this yo-yoing is bad for your health. It results in more weight being carried around the belly and a higher risk for many chronic diseases, along with self-esteem issues. I would urge you to concentrate on developing a healthy lifestyle that keeps you fit, trim, and happy.

While it's possible to lose weight faster, a pound a week is generally accepted as the fastest a slightly overweight person can lose pure fat. If you're losing weight faster, odds are there's some muscle, minerals, and water being lost too.

MFP sets me up at 1240 calories a day and I try to eat that much and I too don't know if I'm getting enough calories. I walk and climb stairs which burn calories. I'm 5'4 at 120 pounds and thats how much calories MFP recommended for me.

My goal is to consume at least 1,200 calories per day. 1,200 is the minimum and you shouldn't really consume less.

Eating food is not JUST about weight. It is fuel (energy) for our organs - our brain, liver, kidneys, heart, stomach, and muscles, for example, all require ENERGY in order to function. Our bodies require nutrients to keep in good condition - organs, nails, hair, vision, digestion, etc. These nutrients come from FOOD. A little at a time. If you do not eat enough, you are depriving your body of the very necessary nutrients it needs to operate.

Want to know what can happen with inadequate nutrients?

http://en.wikipedia.org/wiki/Nutrition#Illnesses_caused_by_improper_nutrient_consumption

Eat. It is as important to eat enough food as it is to not eat too much.