I would think it's the same as the German das vaterland which is a neuter term saying "the land of my father", since Scandinavian languages are essentially Germanic, I would guess the same goes here. But I must admit, never given it much thought. ^_^
Also, in Denmark at least, I have never heard anyone refer to the nation by gender. Except for ships though, but that's not what you meant was it?
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I didn't understand this bit: did you mean that when talking about the fleet of Denmark, one would refer to it as "Her navy", or a particular ship is referred to as "her", as in "her crew"?
Also, Phillip K. D1ck (PKD) specifically reversed the proportions of latin and germanic derivative words in his writing. His works contain words with roughly 90% germanic and 10% classical origins.
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Meta, he meant that ships are referred to as 'her', but not the nation. This is the case for all the Scandinavian countries.