Residence permit from an European Union country

Hi, I am Serge from Holland. I want to marry my Peruvian girlfriend in November. Denmark seems to have the friendliest rules to do so. However, a residence permit from an European Union country is obligatory. Since she is working in Peru now, and will come over for marriage (after which I'll join her in Peru), this is a bit confusing: what forms of valid residence permits from an European Union country do exist?

My latest information is that a stamp in her passport that provides a 90 day entrance to all Schengen countries will do. Since 2016 Peruvians do not need a visa any more, so she will get Schengen entrance by arrival in the EU.

My question: is a 90 days EU entrance stamp in her passport a valid residence permit for marriage in Denmark?

Much obliged for your interest!

Serge and Kathy  :)

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