Proving he's actually still around, and a problem, presumably.
This is not exactly an uncommon trope - the zealous yet underequipped avenger, chasing their prey across the land. Stopping to think about how this will actually play out is not part of the deal, usually.
Though one might posit that given the scarcity of any evidence of activity, they could have expected Sauron to be weakened and isolated, hiding alone somewhere; in which case Galadriel might well have considered herself a worthy match for such an opponent. Or, alternatively, her goal might have been simply to prove that Sauron is still a threat, whereupon she could go to Gil-galad and make a case for a full-scale military assault.
It does make sense, in a way. You don't go searching for an elusive enemy with an entire army. You do that with a small, mobile scouting party. That doesn't mean it's what you use to attack eventually - finding your quarry merely comes first.