Why Moria?

[Formendacil]

Another thing to note is that when they left Rivendell, the Fellowship had every reason to hope that they would be able to cross over the Redhorn Pass- and so into Lorien, which Gandalf apparently intended to visit, re this statement of Aragorn's:

'Our road leads beside it for many miles. For I shall take you by the road that Gandalf chose, and first I hope to come to the woods where the Silverlode flows into the Great River--out yonder.' They looked as he pointed, and before them they could see the stream leaping down to the trough of the valley, and then running on and away into the lower lands, until it was lost in a golden haze.

That being noted, by the time that the Fellowship reached the Redhorn Pass- and found it impassible, going back north was really a non-option. They would easily have lost a couple of months going back and then down the Vale of the Anduin- even if, as Kuruharan notes, there was no Dol Guldur to worry about.