Wouldn't the appropriate time for Eowyn to dramatically whip off her helm and proclaim her womanhood be after slaying the Witch-King?
That kind of prissified battlefield hubris should be unsurvivable. Realistically, the result should have been: "I am no Wo-ghlurkkk!"
No, girlie. First you kill, then you gloat. Spitting on your fallen foe is optional.