"When is your birthday?"
Translation:Ngày sinh của bạn là ngày nào?
Yes, "... là khi nào" would be correct here.
"Khi nào" is an adverb of time. A rule of thumb is, if you remove an adverb, the rest should still be a complete sentence (maybe not meaningful, but still correct by syntax). "Ngày sinh của bạn" is just a noun phrase, it lacks verb to be a full sentence. So there should be "là" there.