I think that Frodo knew that no one else could have possibly carried the ring, for the above reasons. Also, I believe that Gandalf was mildly surprised at the strength and ability that the little hobbits had, or else the four of them would not have survived. However, it was Gandalf who gave Frodo the quest, even though it might not be percieved this way. I think Gandalf knew of no one else that could handle the task, so he let a hobbit do it. Frodo was merely carrying out Gandalf's wishes, Gandalf was the one who set him out from the Shire in the first place. In fact, didnt he do the same thing to Bilbo too?
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