“The condition of women in a nation is the real measure of its progress.”

Special message to the Congress on National Health Needs (65)" (27 February 1962) http://www.jfklibrary.org/Research/Research-Aids/Ready-Reference/JFK-Quotations.aspx
1962

1940s, Third Inaugural Address (1941)
Context: Lives of nations are determined not by the count of years, but by the lifetime of the human spirit. The life of a man is three-score years and ten: a little more, a little less. The life of a nation is the fullness of the measure of its will to live.

Diary(27 February 1890)
Diary and Letters of Rutherford Birchard Hayes (1922 - 1926)

Widely attributed to Gandhi, sometimes citing Ramachandra Krishna Prabhu, The Moral Basis of Vegetarianism (1959). (Cf. Ralph Keyes, The Quote Verifier (2006), p. 74.) However, it is not found in that essay http://www.mkgandhi.org/ebks/moralbasis_vegetarianism.pdf nor in any of Gandhi's Complete works. http://animalsmattertogod.com/2013/09/13/mahatma-gandhi-hoax-quote-greatness-of-a-nation-and-its-moral-progress-can-be-judged-by-the-way-that-its-animals-are-treated/
The original quote seems to be by David Strauss, The Old Faith and the New (Der alte und der neue Glaube, 1872, trans. by M. Blind, New York: Henry Holt & Co., 1873), vol. II, ch. 71, p. 59 https://archive.org/stream/oldfaithnewconfe01stra#page/59/mode/2up: The manner in which a nation in the aggregate treats animals, is one chief measure of its real civilization.
Similar quotes, not attributed to Gandhi, are found throughout the twentieth century: e.g. The great actress, Mrs Fiske, once said to me, "The civilization of any country can be told by the way it treats its animals" (Zoe Berkeley, "Zoe Berkeley's Corner", Salinas Index-Journal, 1933-07-01, p. 8).
Attributed to Gandhi since at least 1980: The seal hunt truly is Canada's shame and we would do well to think of the words of Gandhi when he said, "The greatness of a nation and its moral progress can be judged by the way its animals are treated" (Doris Potter, Letter to the editor, The Gazette (Montreal), 1980-03-18, p. 8).
Disputed

2000s, 2000, A Continent Bleeds (2000)

No. 30
The Federalist Papers (1787–1788)

2015, Young African Leaders Initiative Presidential Summit Town Hall speech (August 2015)
Context: The best measure of how a country does economically in terms of development is how does it treat its women. And as I said in a speech -- a couple of the speeches that I gave while I was in Kenya and Ethiopia -- if you’re mistreating your women, then you’re just holding yourself back, you’re holding yourself down. You may have some false sense of importance, but ultimately you don’t benefit if women are being discriminated against, because that means when they’re working, your family is going to have less income. If they’re not educated, that means your children are less likely to be well educated, because, typically, the mother is the first educator of a child. So if they see you disrespecting your wife, then what lesson is your -- not just your girls, but what lessons are your sons learning from you? […] You do not lift yourself up by holding somebody else down.