Hi Alicia, you raise a very good point. I am on the smaller side myself, so I know it is frustrating to burn fewer calories than others do.
The 1200 is the magic number under which people think your body starts to slow down to conserve energy--the "starvation mode" hypothesis. To the best of my knowledge, it has neither been proven nor disproven. There are people on this site who have experienced a slow down or stop in weight loss when dipping below a certain number of calories. There are also others who have gone well below it and not experienced a slow down. This leads me to conclude that it's an individual thing.
I would suggest trying different calorie intakes for a couple weeks at a time to see what you can sustain and how you lose the best. The logs make it easy. It may be that you just need to take a slower road to the overall loss because it is harder to manage a significant calorie deficit when your overall burn is relatively low to begin with.
If you don't have a lot to lose, that makes it a bit harder as well.
But it is do-able. The tools here and the people make it easier.