It is not correct. Subjects of sentences can be identified as nouns, pronouns or correlatives which don't have a preposition before them, and no -n ending. That sentence structure would incorrectly suggest that both vi and kiu are subjects.
The only subject in that phrase is vi, so kiu takes the -n ending.
The same would apply in variations of the question, such as:
"Vi amas kiun hundon?"
"Vi amas kiun vian kolegon?"
and to possible responses, such as:
"Mi amas tiun"
"Mi amas neniun"
"Mi amas la princon"
There are cases when a preposition would indicate that kiu is not a subject, in that case no -n is needed:
"Vi parolas pri kiu?"
"Vi kuras al kiu?"
Or, if kiu would be a subject (who loves you?) then vi gets the -n: "Vin amas kiu?/Kiu amas vin?"