[Neferchoirwen]

I think that it's okay to say that the Fellowhip is really Frodo's Fellowship. The quest was his in the first place. Since it's no small chore that Frodo takes, all of Middle Earth with him. with its fate resting around his neck. So it is proper for 8 other people to take on the quest with him.

At the very end of the story, though, we see Frodo naked. What I think about that is that Frodo confronts his task alone for the first time, in the middle of it all. Now that he is at Mordor, he may turm his back on the quest now that he finds that he has survived it and thinking that not "all that."

At that "naked moment," the choice of giving up the ring to the fires of Mordor lie solely on Frodo. It's his decision in the end, and no matter how pure he is, as a Hobbit far removed from the "outside" world, the Ring chooses no one and corrupts nevertheless. Had the entire Fellowship been there, then it would have been chaos with everyone arguing about who should throw it in and who shouldn't, or worse: who should finally keep it and kill everyone in the end.

So to answer your question, Frodo does looks into the Void on his own. He is the Ring bearer, and he has to face the task of facing the Void. The Quest that he finishes brings him to himself. All of the Fellowhip have other things to fulfill, and he is left alone.