If you're underweight because you don't eat enough then that's something you should think about, but it doesn't mean you have an eating disorder. I think, at least for anorexia there has to be a FEAR of being 'fat'. I think it would help to look at the REASONS you're underweight, why do you not eat enough? Or do you eat enough and you're just naturally underweight? (some people eat normally or even a lot and maintain low weights).
If you're worried about food and weight and your eating is as a consequence to those worries, then it could be an eating disorder.
I'm not a doctor though, so if you're worried maybe ask a doc. But no, being underweight doesn't mean you have an eating disorder. Same as being overweight doesn't mean you have one.