I think that Elrond, like Gandalf, saw the "strong side" of hobbits. He might have half-known-half-guessed that only hobbit would be able to take the task.
*That made me think of this - Elrond to hinself: "Only a hobbit would be strong enough - or stupid enough - to do this..."
*
And, as has been said before, both Elrond and Gandalf probably sensed that Frodo would have to go. Bilbo did too.