"What country is she from?"
China is very homogenous and racially driven, because of this the concept of nationality is very much tied to race and the country of origin. If you ever immigrate to china, it is unlikely most people would acknowledge you as "Chinese" nationality, even if you live there for 50 years and undergo naturalization. In their eyes you will forever be a Loawai.
As soon as you have an interrogative word (which = 哪, who = 谁, what = 什么, how = 怎么样 ...) you drop the 吗. 吗 is only used to distinguish questions without interrogative words from normal sentences. In English, the words change their positions in the sentence:
Mum is well. - Is Mum well?
In Chinese, you have the 吗 for that:
But as soon as you have an interrogative word, the 吗 is dropped:
How is Mum? - 妈妈怎么样？
Yes. 哪 means "which" and is only really ever used to modify something. Think of 哪国 as one block, meaning "which country". You're not literally asking "where" she is from, you're asking what "-ese" she is, if that makes any sense. (Chinese? Japanese? Vietnamese? Burmese? ...She's a person from what country/哪国?)
Easy mistake to make: You used 那 when you wanted 哪。
(I’m guessing it’s just an oversight - forgetting to include the square on the character - but in case it helps someone: 那 nà means ‘there’, a statement, whereas 哪 nǎ means ‘where’, a question.
I.e. 她是哪国人=she is what nationality? ; 她是那国人=she is that nationality.)