Yes it should be accepted, but I think it is by now?
@Natalino4ka: You're right, that "zum" includes a definite article and hence would have to be translated using "the" instead of "a". However, in THIS case, if someone says "Ich gehe zum Arzt", it doesn't necessarily mean they're going to a particular doctor - it just means they're going to a doctor. It's a common phrase. Therefore, in this case, "I don't want to see a doctor" is a perfectly fine translation.
I'm not a native German speaker, but -- most often the verb goes after the finite verb: "ich will nicht zum..." meaning "I don't want to go..."
You can move the "nicht" to change the emphasis, and make it clear that the negation is about some other element in the sentence, but that just doesn't work here -- "will nicht" is really a single idea, and moving "nicht" away from "will" would just weaken the sentence and make it sound funny.
There's some good information about German word order in the following link -- search down for "placement of nicht"
You can't. "'Nicht' precedes what it negates" (https://yourdailygerman.com/position-nicht-german/).
"Ich will zum Arzt nicht" is like saying "I want to go to the doctor not".