Did Elven women stay at home? No. Indis wandered around Valinor singing and tending to plants and trees in the wilds. Luthien went off dancing in the woods of Neldoreth and did who knows what else until Beren came along. And then she went after him and saved his bacon more than once (he saved her a time or two).

Idril was the Elf who had the "Way of Escape" built out of Gondolin.

Haleth led her people across Beleriand to Brethil and ruled them until she died. She and other women among her folk were apparently amazons, female warriors.

Emeldir the Man-hearted saved the last remnant of her people by leading them through the mountains of horror to refuge in Brethil.

Erendis stood up to Aldarion though in the end she became petty and bitter, but their daughter Ancalime became the first ruling queen of Numenor, a not-so-insignificant fact.

Eowyn was a trained warrior who permitted her despair to drive her to seek death, and instead she found greatness and new outlook on life.

Galadriel left Beleriand before Morgoth overcame the Eldar and destroyed their kingdoms. She was a mover and shaker in the Second and Third centuries and she was responsible for forming the White Council (in the book, not this board). She travelled around the map and doesn't seem to have done much staying at home. Yes, she sewed, and so did Arwen, but they did this by choice. Galadriel and Arwen, as the chief women of their communities, were also probably the equivalent of high priestesses, overseeing the raising and harvesting of the crops, the preparation of food, and the healing of the injured or careworn among their peoples.

There are many examples of how women not only didn't just stay at home in Tolkien, but how they took action and had a great impact on their world.

Tolkien seems to hold women up as equals to men in many ways, but also he extends to them a romantic wisdom and perception which the men lack. No woman ever leads her people into folly in Tolkien's world, and only the men are responsible for the dooms which befall their people.

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Parma Endorion: Essays on Middle-earth, Revised Edition