Will my future wife have problems getting a green card if she overstayed a previous visa?

The bar for overstaying most visas for one year or more is 10 years. You say that she overstayed by about one year. If less than one year, she was only barred for 3 years and would be eligible to immigrate. If her overstay was a year or more, that would be more troublesome. Assuming that situation -  as your fiancée has already returned to Peru for eight years, she can either wait that period of time before appearing for interview at the American Embassy or she can appear before that time and also request a waiver of the bar. I note that the waiver would be based upon extreme hardship to you. In submitting a petition for your fiancée, you can of course submit at any time, and the ten year bar issue would only arise when she is interviewed for the K-1 visa. Due to the limitations of the lawyers.com forums, Alan Lee, Esq.’s (the firm) participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting the question. No attorney/client relationship is or shall be construed to be created hereby. The information provided herein by the firm is general and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice, nor as the basis for making any decisions of legal consequence.