From a grammar book:
- Hun er her/der ikke = unstressed "her/der"
- Hun er ikke her/der = stressed
- Her/der er hun ikke = heavily stressed
I.e., various word orders are correct for this and similar sentences, depending on the stress. Without further context, it's probably the safest to assume the unstressed answer should be the one they're after.
I get your answer, but the word order still seems odd to me. I guess because in English and German ("Sie ist nicht hier.") it's the same, and Danish is the odd man out. But I'll get used to it, and I'll have to keep my eyes open for other examples of other adverbs which have a Danish sentence placement different from German.