I don't think you can say across the board that all gifted kids need a lot of interaction. Both of my kids got a lot of interaction as infants and toddler, whether they wanted it or not, because that's just who I am. But as they've developed into little people (DD10 and DS7), they are very different. DD wants a lot of interaction. DS is happy to entertain himself for hours. He talks constantly, but not necessarily looking for a response.
And while DS hasn't been tested, I suspect that he has more natural intellect than DD, although DD is more ambitious and self-motivated and will probably perform at a slightly higher level.
I'm sure you know that you can't "teach" your child to be gifted. She either is or she isn't, and the best thing you can do is follow her cues. As she grows, answer her questions, or help her find the answers. Indulge her curiosity, and give her the opportunity to explore her interests. And for now, if she wants to entertain herself, just enjoy that. After DD, who we joke is like gum on my shoe, I was thrilled to have a child that didn't need constant interaction.