The verb å gå can be used for the verb "to walk", but it can also be used for the English verb "to go". In this instance, gikk is not the past tense of walk, but the past tense of go -> went.
Therefore, the sentence reads in English: "It WENT well thanks to the doctor".
You would need the larger contextual clues of the situation, but given that the sentence was "det" rather than "hun" or "han", it doesn't obviously seem to be directly referring to a person as the subject. So I would assume the translation to be "went" rather than "walked" without some very specific context to inform me otherwise.