Upon entering the US, before the marriage takes place, she will be considered a non-immigrant with temporary status for up to 90 days.
The day you get married she is considered a "conditional" permanent resident. Now her intent should be to stay in the US and apply for full permanent status. If she wishes to return to study it is at this point she should return back to Peru. She'll lose her conditional status in the process and need to apply for one of two visas if she wishes to enter the US again. 1) Tourist Visa or 2) Permanent Residency as a spouse of an American Citizen.
If, after marrying, she wants to change her conditional status to full permanent status, then she wont' be able to leave the US while waiting for this visa for extended time periods without risking losing the application and having to start over.
I'm not immigrations expert but I have read quite a bit on the topic.
-- Now here are my totally subjective opinions:
So yes if you really want to get married now then do the fiance visa, get married, and she should return back to Peru immediately and finish schooling. Come back when she's ready to live in the US on a residency application as a spouse of a US citizen (FORM I-130). I can only imagine though that this will be a bit complicated and require a lot more red tape BS than it's worth and more $$$. You'll have fees for the K1 and the I-130.
My advice is don't get married yet if she's not ready to stay here permanently. Just wait!