Frodo's initial task was just to get The Ring to Rivendell, after all.

(Smash cut to Frodo and Sam clawing their way up Mt. Doom)

" 'Ah, just take the Ring to Rivendell and I'll catch up with ya! ' he said.

'Elrond's pretty sharp he'll know what to do!' he said.

'It'll be an aDvEnTuRe!' he said!"