I think Galadriel probably sensed the fight between Gandalf and the Balrog, and ultimately knew that Gandalf survived. None of the Wise could ignore a conflict such as that, since two Maiar haven't fought like that since the First Age (most likely). If not that, then Galadriel could probably "mind-speak" with Gandalf, becuase at the end of Return of the King, when everyone was leaving Minas Tirith, they constantly talk to each other mind-to-mind. If they could do it then, it makes sense that they would be able to do it about a month/a few weeks before.
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But Melkor also was there, and he came to the house of Fëanor, and there he slew Finwë King of the Noldor before his doors, and spilled the first blood in the Blessed Realm; for Finwë alone had not fled from the horror of the Dark.
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