Translation:The doctor is going to receive the results tomorrow.
While the present tense can refer to near future events (making your sentence theoretically possible) there would be no preposition "a." The "to" you are suggesting is not a directional "a" as in "goes to Spain - va a España" but is instead either part of an infinitive verb "goes to receive - va recibir" or a preposition of reason "goes [in order] to receive - va para recibir." I can't guarantee that this is how a native speaker would express this though. Regardless, the inclusion of the "a" here in an ir + a + infinitive structure tells us this is the informal future: "va a recibir - is going to receive."
On a side note: "The doctor" is a medical practitioner; "The Doctor" is a timelord :)
The "is to" structure is used to state a future requirement: "He is to bring his money" - "He is to go to court." Crucially, it places onus on the subject to perform the verb. So, when you say "The doctor is to receive the results tomorrow," technically you're saying "The doctor is required to receive the results tomorrow." Of course, in conversation, your sentence would more likely be interpreted as "The doctor is going to receive the results tomorrow," but DL can't be expected to accept all answers that are conversationally acceptable.
I worte The female doctor is going to receive the results tomorrow. And was marked wrong - the correction was: The family doctor is going to receive the results tomorrow. And from where comes the family there? Does Dou roll a dice or just guess or what? There is no familiy in the Spanish sentence!
Ok, so firstly your translation is not wrong. DL marks it wrong because unless there is a specific reason to identify the gender of the doctor we wouldn't say "female doctor" or "male doctor": While Spanish identifies the gender inherently in the noun we do not have to (and shouldn't without a specific need) include the doctor's gender in our English translation.
Secondly, DL offers alternative answers based on the closest matches in their database, which would be why they corrected your "female" to "family." Probably "family doctor" was included in the database as a more specific option. "Doctor" in both languages is a very general term, but normally it refers to a GP or as some people say a family doctor (as opposed to a surgeon or a specialist of some kind).
So technically your answer is right and their alternative is not perfectly literal, but hopefully this explains why they corrected you the way they did.