It was in origin Bilbo’s private diary, which he took with him to Rivendell. Frodo brought it back to the Shire, together with many loose leaves of notes, and during S.R. 1420–1 he nearly filled its pages with his account of the War.
Interesting how Tolkien is more interested in presenting and maintaining the framing narrative than he is keeping a sense of suspense -- he is establishing before the story starts that Frodo will survive.

