During the time of the Fellowship, Elves and Dwarves weren't exactly the best of friends and this has been depicted by Legolas and Gimli. However, they eventually develop an incredibly strong friendship.
When was the first moment in which these two characters began to respect and trust each other?
I am looking for sources from the novels.
Although we're not given a great amount of insight into Legolas and Gimli's burgeoning friendship, this is clearly the time it begins (emphasis mine):
Legolas was away much among the Galadhrim, and after the first night he did not sleep with the other companions, though he returned to eat and talk with them. Often he took Gimli with him when he went abroad in the land, and the others wondered at this change.
Fellowship of the Ring Book II Chapter 7: "The Mirror of Galadriel"
The Company was arranged in this way: Aragorn, Frodo, and Sam were in one boat; Boromir, Merry, and Pippin in another; and in the third were Legolas and Gimli, who had now become fast friends.
Fellowship of the Ring Book II Chapter 8: "Farewell to Lórien"
