There are many quotations that suggest she is not a mortal human being, but in fact a nature spirit or a Maia.
From The Adventures of Tom Bombadil:
"Go down! Sleep again where the pools are shady
far below willow-roots, little water-lady!"
She is clearly able to live IN the river, but also on land, suggesting that she is not completely human.
From The Lord of the Rings:
"But I see that you are an elf-friend; the light in your eyes and the ring in your voice tells it."
Here Goldberry recognises the goodness in Frodo, but makes an allusion to the one Ring, hearing its power working on Frodo as she speaks to him as she has not yet seen it. Her and Tom both seem to sense the ring and perhaps see the 'shadow' realm, meaning that they are more than simple humans living in an ANCIENT forest.
I think it unlikely that they simply humans. Her singing, for example, is described "as young and as ancient as spring". Personally, I believe that she and Tom are nature spirits, sent to act as protectors for the diminishing natural world. They live in 'The Old Forest' which many find an unpleasant place, which makes me believe that they have lived there since before corruption made the trees hateful, otherwise they would encounter many problems.
Furthermore, Goldberry's voice implies that she has lived close to the birth of the river, and has seen it through many seasons, giving her the appearance-and voice- of a youthful woman wise beyond her years, when she is in fact, immortal. She also states that Tom Bombadil 'Is', meaning that he just exists, and is tied to the land. As the world around us simply 'is' there, so is he, and he will only die when it 'is not'.