The sentence with to be is correct. I am sure there is an easy way to explain to versus for, but I am not an English teach and will not try to explain all if the differences between the two words. However, to be is used for future tenses while being is a present continuous tense. You are expressing a future aspiration so you want to be a doctor. If you were already a doctor you could say, For being a doctor, one must have studied a lot. However, this is awkward and unnatural. It would be more appropriate to say, to become a doctor, I had to study a lot.

This rule isn't always true, but it is very often true: to + verb = your goal or objective for + verb + ing = a feature, function, or use of something I'm studying TO BE a lawyer. (My goal is a job as a lawyer.) This app is FOR FINDING good restaurants. (That is how you use the app.) Is the difference clearer now?

I've studied to be a doctor. I can be confusing especially if you are translating it literally from the spanish language. Sometimes you just need to learn it that way and not forget it. I believe that would be the best way possible. For example Your sentence, in spanish would be, He estudiado para ser un doctor, please excuse me if i'm wrong. Literally it would translate to, I have studied for to be a doctor, But its actual meaning is I have studied to be a doctor. From the word Ser we interpret it to be to be, haha. Quite confusing, i hope i didn't confuse you. Anyways hope it helps a little bit