Hey, Eldar, welcome! :)
Nope, she's not an elf. She (like Tom) might be one of the Maiar, but that's not really clear. She seems to be some sort of water-spirit, like her mother (since she's called the "River-daughter"). I always pictured her like a classical water nymph, like Daphne only without the whole tree thing. Goldberry's origins are pretty mysterious though (not unlike Tom's really. Fun couple).