The English is perfect, admittedly a bit literary. "Vocation" is actually the precise translation for the German "Beruf" You have the root "vocare" -to call like the german "rufen".
The sense here is that "Er fühlte sich zur Medizin berufen".

rather "Berufung"

Yet "Berufung" is something, that exists independent from my will. In German we can say "Ich mache etwas zu meinem Beruf", but we can't say "Ich mache etwas zu meiner Berufung". We say for example: "XXX ist meine Berufung." or "Ich sehe meine Berufung darin," (dies und das zu tun).
Conclusion "vocation" may be translated by "Berufung", but not in the above sentence, where the translation hast to be "Beruf".
Nevertheless Dejo is completely right, when he is using "Berufung" to derive the meaning of "Beruf".

It turns out that "vocation" has 2 meanings: 1. a calling, 2. the occupation itself.
vo·ca·tion
/vōˈkāSHən/
Noun
A strong feeling of suitability for a particular career or occupation.
A person's employment or main occupation, esp. regarded as particularly worthy and requiring great dedication.
Synonyms
calling - profession - occupation - trade - metier

I conclude that the above sentence is correct, although I would have said "profession".

[Putting the Japanese sentence through Google translate gives you " I decided to be a doctor."

You might also note that Zifre is a native speaker of English:)