Small hands do them because they must...

[Galadriel]

"The road must be trod, but it will be very hard. And neither strength nor wisdom will carry us far upon it. This quest may be attempted by the weak with as much hope as the strong. Yet such is oft the course of deeds that move the wheels of the world: small hands do them because they must, while the eyes of the great are elsewhere."

I actually took that as an encouragement to common folk, not to Frodo in particular. I think Gandalf is implying that it would not make much difference if a Hobbit or an Elf took the Ring, since its power could ultimately control any being, and that perhaps the folk that had been hitherto neglected in history would be brought to the light because the 'greater' people simply would not do the most difficult task. If anything, I think he is praising the Hobbits for their valour, and also for their willingness to go into peril even though they are not directly related to Sauron or the Ring (save Bilbo's act of picking it up).