Two clarifications, one about the structure, the other about the measure word.
1) The structure
Subj. + Verb + 哪个 (+ Noun) ?
The above structure cannot be generalized and applied to all contexts. It's just an example. Another example structure can be:
哪 (+ Noun) + Verb + Object?
As you can see, in the above structure, the interrogative particle 哪+Noun is the subject of the sentence.
2) The measure word
The measure word 个, as well all other measure words, is not related to the interrogative particle 哪, but to the noun. I mean that you could also need to say, for example, 哪位, 哪些, 哪台, 哪本, etc. according to the measure word the following noun needs.
You could also say 你是哪个国家的人？But I would prefer the already commonly used shorten form 哪国人.