Jean Kerr wrote a semi-autobiographical bestseller called "Please Don't Eat the Daisies" which was adapted into a motion picture in 1960 starring David Niven and Doris Day. It has similar plotlines as "Critic's Choice" - a theater critic is married to a writer and they move into the country. He has to review their best friend's new play while fending off the attentions of a Broadway actress - mayhem and hilarity ensues. Niven and Day were better cast as critic and playwriting wife than Hope and Ball.
Getting back to the topic at hand - Doris Day had more skill and range than she has generally been credited for. I think she would have scored in the leading role in the film adaptation of "Mary, Mary". Also, a freer adaptation with a quicker, bouncier pace would have resulted in a better picture.
I am also of the opinion that Doris Day should have done "Forty Carats" as well which was offered to her and turned down. Liv Ullmann was too young and all wrong. I also think she should have been Nellie Forbush in "South Pacific".
Doris started out as a band singer which is live performing. Did she ever do stage work?