June 3, 1991

The lady is Eva Le Gallienne (January 11, 1899  to June 3, 1991), the poet's daughter. We don't know the name of the cat. Le Gallienne was an actress. Here is a sketch from her New York Times obit:
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On the strength of.... encouragement from theater folk, Miss Le Gallienne and her mother left wartime London in 1915 for New York. Her bright expectations were not immediately realized. ....

Finally, at the age of 20, she enjoyed her first big success, opposite Sidney Blackmer in Arthur Richman's "Not So Long Ago." This was followed by a still greater hit in 1921 with Joseph Schildkraut in the Theater Guild's production of Molnar's "Liliom."

In 1923, she had another hit in the star role in "The Swan" by Molnar. During its long run in 1923 and again in 1924-25, she became obsessed with the need for a repertory theater.

"Miss Le G.," as generations of theater people called her, came closer than any other person to endowing the United States with a permanent company performing repertory in the manner of the Old Vic, the Comedie Francaise and the Moscow Art Theater. [Her multiple attempts failed due to financial constraints.]
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With her longtime companion, the late actress Marion Evensen, she moved to the estate at Weston, which she had bought at a prosperous time in 1926. There, with barnyard and forest creatures, cats and a kennel of cairn terriers, she busily gardened, wove, wrote and studied for the rest of her life -- but never abandoned the theater.
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During the war years, the actress also toured for the Guild as Mrs. Malaprop in "The Rivals" and returned to Broadway as a star opposite Joseph Schildkraut in two successes: "Uncle Harry" by Thomas Job and a new "Cherry Orchard." She had also produced the play and helped to translate it.
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Another memorable role was her performance as Queen Elizabeth in Schiller's "Mary Stuart," which she did on stage across the country periodically from 1957 through 1962, and also on television.

As translator, director and a star of Chekhov's "Seagull" in 1964, Miss Le Gallienne received from Adlai E. Stevenson the award of the American National Theater and Academy. ...

She was ...[in 1977] on tour, in "The Royal Family." The revival of the Edna Ferber-George S. Kaufman comedy based on the Barrymore family was a hit of the 1976 Broadway season and a triumph for Miss Le Gallienne, who played the mother of the tribe, skipping girlishly upstairs in Act I and descending like an elderly queen in Act III.
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In 1986, President Ronald Reagan awarded her the National Medal of Arts.

Miss Le Gallienne traveled everywhere for many years with a two-pound Yorkshire terrier, Nana, in a little basket.

....." She ... translated "Seven Tales by Hans Christian Andersen" and wrote a biography, "The Mystic in the Theater: Eleonora Duse" (1966).

More information is available here, where I found the photo,