Actually, I don't think it would be healthy for you, it sounds like you are eating too little as it is, and removing even more nutrients from your body would be bad, you need some fat to be healthy, and I'm not sure you get enough as is.
I'm sure I won't be the only one to say this, but 1200 is WAY too low, especially for someone who works out, and I know if you are working out to Cathe, then you are WORKING OUT!
It might take a leap of faith, but you may want to start to increase your calories, with all healthy foods of course, you really should get out of the habit of 1200 a day. If I can stay around 1700/day, I seem to lose (super slow btw, it's been like a pound a month), but I like to eat. I maintain in the 2000ish range.
I really don't think Alli is the answer for you. You could just to make sure, look into going to a doctor that specializes in hormones and thyroid and get a full workup done to make sure it's not something like thyroid.
You could also check out something like the GoWear fit, so you can track your food intake AND see the calories you really burn everyday.