There is a connection between the very first beginning of The Hobbit and Frodo‘s and Sam‘s rest in Ithilien.

Tolkien‘s famous very first words as written down on a student‘s paper were »in a hole in the ground there lived a Hobbit«. In German I first read »In einem Loch im Boden lebte ein Hobbit« – and there is nothing extraordinary about these words. It just seems to be an invention. The start of a playful story.
But the thought struck me that »in a hole in the ground there lived a RABBIT« would be an everyday sentence. And considering the authors sense of humor and his creative game with language I can easily imagine how much he loved transforming an everyday meaning into something beautiful, mysterious and funny by just changing two letters: Hobbit!
When the story line grew and – like a river – floated into the epic history of Middle Earth there still remained a certain relation between rabbits (the smaller hare) and Hobbits (the smaller people).
In Ithilien the original children story of Bilbo and the dwarves had become a kind of passion tale. And suddenly the darkening story turns into some kind of rest. Frodo and Sam on their way of self sacrifice enjoy a meal provided by the miserable and treacherous creature Gollum: Two stewed rabbits.
A meal which opens the way to the sacrifice (later in Mordor Sam tries to recall the memory of this meal to his master) and at the same time saves their lives by drawing the attention of Faramir’s troups to the Hobbits.
This is a meal of comfort and of rescue.
But it is not a vegetarian, »innocent« meal like eating some bananas. I think it is not by chance that these two rabbits get killed by Gollum. I cannot help but feeling the relief for Sam and Frodo and at the same time the deep pity for those little rabbits which get killed by Gollum in a way I don‘t want to figure out.
Without being allegorical there is such a closeness to the Eucharist. Those two rabbits here really represent the two hobbits giving their lives for those who eat them. 
So they ›got up and ate and drank. Strengthened by that food … they traveled‹ to Mordor. (cf. 1 kings 19.8)