I can explain why: in German (and scandinavian languages) the verb always comes in second position, so when something is put at the beginning of the sentence, the verb will come immediately afterwards, and then the subject follows after that. In English, however, the subject ALWAYS comes before the verb (except in questions, where the verb comes first in all these languages).
The basic sentence in this case is "Everything is perfect", and in German, "alles ist perfekt". When emphasising the prepositional phrase "at the doctor's" by putting it first, the German sentence MUST change the word order so that the verb comes in the second position, and the English sentence MUST keep the original word order.
The subject does not always come before the verb. In English we use inversion in quite a few places too, not just in questions, and I would say that this is fine in this example.
Non-question examples with inversion:
"Only after seeing that did I believe it."
"Never would he do that."
"Into the tree flew three birds."
It's probably the distinction between doctor and doctor's. However, it could also be the change in emphasis/connotation that is caused by the change in word order. "Everything is perfect at the doctor's" emphasises the perfection of everything while "Everything at the doctor's is perfect" emphasises the at the doctor's. The former would usually be used to, for example, tell someone that it is a really good doctor's surgery. It would also work if reversed to use similar word order to the German phrase ("At the doctor's everything is perfect"). I don't know if Duo accepts that version though (it probably should if it doesn't). The latter would usually be comparative or used as a counter example (e.g. someone says "Everything in this part of town is really dirty", to which you reply "Everything at the doctor's is perfect"). There are of course situations in which either could be used, although it would still change the emphasis. Could a native German speaker chip in on the subtleties in the meaning please?
I already read the comments, but it looks lame to me.
At the doctor's everything is perfect. so does it mean 'everything of doctor' or 'doctor is everything' ?
it looks like possessive rather being 'is'; even though it doesn't make sense saying 'at the everything of doctor is perfect'. what thing?