The hero's journey is the description of the transformation of a character from an ordinary person to a hero. The hero-in-the-making passes through a series of trials, transforms himself with some great feat, and returns home.
In the hero’s journey megamyth, the “road home” involves the hero’s journey home after being reborn through his adventures. In “The Fellowship of the Ring,” we actually only have one third of the journey. The real road home does not occur until after Frodo throws the ring into the volcano, destroying it for good.
When Frodo and his friends return home in “The Return of the King,” they actually have to fight another battle. The Shire has been transformed, and is overrun with orcs. The hobbits have to fight them and get the other hobbits to fight before they can return to a more normal life.
However, there is a sub-arc in “The Fellowship of the Ring,” where Sam and Frodo get separated from the rest of the fellowship. They witness the battle and see their friends Merry and Pippen taken. At this time, Frodo (the hero), decides he must go off on his own. His faithful companion Samwise catches up with him. Sam knows what Frodo has to do.
He's off to his home, as he always said; and no blame to him. But Mr. Frodo, he knows he's got to find the Cracks of Doom, if he can. But he's afraid. Now it's come to the point, he's just plain terrified. (Ch. 10)
So while the journey to take the ring to Mordor is not really the road home, it is a road that Frodo travels after accomplishing something. He has separated himself from the group, and decided to go on his own. This is brave, because he is afraid of what might happen if one of his company turns on him and takes the ring, so he acts as he needs to. Sam accompanies him through his own grit, but Frodo did attempt to go on his own.