I like your point.... Aragorn looks to Frodo as the leader, and after that it seems like once Frodo takes on the responsibility of trusting Strider, the other hobbits defer to him. It is an interesting transfer of authority, and rather subtle. Frodo may be deferring to Aragorn on the overall decisions, but he's the one that decides that all of them need to follow Aragorn's lead. Very interesting dynamics indeed...
I also think, though, that Frodo makes a major leap in his taking on the role of leader when he leaves the fellowship and he and Sam go off on their own. But this portion of the story is where he starts heading in that direction, I think.
I also think, though, that Frodo makes a major leap in his taking on the role of leader when he leaves the fellowship and he and Sam go off on their own.And that is why in the film, Gandalf thrusts the Moria decision upon Frodo. He knows (or suspects) that the Fellowship will eventually break, and that Frodo will need to be able to take decisive action.