Found this. She was in the Navy.
https://www.findagrave.com/memorial/159990002/rosalie-carol-davidson
Born in Paoli, Indiana, she lived in San Diego, California.
From "Contemporary Authors":
Contributor to Grade Teacher.
CAREER:
Seagram's Distillery, Louisville, KY, in quality laboratory, 1941-43; public school teacher in Denver, CO, 1948-50; Grant School, San Diego, CA, first grade teacher, 1950--. Military service: U.S. Navy, Women Accepted for Volunteer Emergency Service (WAVES), chief storekeeper, 1943-46.
Sidelights
Rosalie Davidson writes: "I wanted to be a journalist, but observed a first grade class in Denver, fell in love with the children, and went back to school to get a degree in education. I taught a third grade summer class of boys who were poor readers. I asked them what they wanted to read about. They said `Dinosaurs!' So I read about dinosaurs--told them each day what I'd read....We each wrote our own dinosaur book! I feel that many science books talk down to primary children, or try to entertain them with funny things. Children want to know the facts, that's entertainment enough for them. I have worked with children for twenty-nine years. I understand their reading vocabulary, their interests and the importance of helping them develop accurate concepts."
About "Who is Root Beer?":
"Four insects, Bee, Ant, Bug, and Butterfly, find an empty root beer can and, in their search for its owner, become fast friends."
https://www.google.com/search?biw=1284&bih=857&tbm=isch&sa=1&ei=OMbqXZDbGIuY_QamgruoBw&q=books+%22rosalie+davidson%22&oq=books+%22rosalie+davidson%22&gs_l=img.3...2256.4619..4845...0.0..0.89.278.4......0....1..gws-wiz-img.8zT1bRBC21c&ved=0ahUKEwiQ1-j4-aHmAhULTN8KHSbBDnUQ4dUDCAY&uact=5#imgrc=_
(some book covers)
https://www.amazon.com/Wont-Dragon-Roar-Imagination-Book/dp/0811644073/ref=sr_1_6?qid=1575666988&refinements=p_27%3ARosalie+Davidson&s=books&sr=1-6&text=Rosalie+Davidson
(review of "Why Won't the Dragon Roar?")
WRITINGS BY THE AUTHOR:
For Children:
Frisky Pup Says - What a Surprise (fuzzy book line) by Marie Hibma Frost, 1968.
("The Pup doesn't want to run errands with his Boy so he runs off to play with his friends. When he can find no one to play with, he returns to his Boy and follows him home where a Surprise is waiting for him!")
Dinosaurs: The Terrible Lizards, Golden Gate, 1969.
(Illustrator) John McInnes, Who Ever Heard of a Tiger in a Tree, Garrad (Champaign, IL), 1971.
("After a frightening journey into the woods, Toy Tiger learns that there is no place like home.")
We Like You Timmy Turtle...little Marcy and Her Friends, 1972
("Timmy learns to be himself - based on bible verses, adapted for children.")
When the Dinosaurs Disappeared, Golden Gate, 1973.
(Illustrator) John McInnes, Drat the Dragon, Garrard (Champaign, IL), 1973.
("A young dragon proves his bravery when he rescues a little girl who falls in the lake.")
(Illustrator) Wayne Carley, Color My World, Garrard Publishing (Champaign, IL), 1974.
("A cat describes his activities in a colorful world.")
The Tricycle Book (Golden Shape book) by Mariellen Hanrahan, 1975
(Illustrator) Norma Q. Hare, Who Is Root Beer?, Garrard Publishing (Champaign, IL), 1977.
(Illustrator) Rosalyn Rosenbluth, Why Won't the Dragon Roar?, Garrard Publishing (Champaign, IL), 1977.
("A young dragon who won't roar, breathe fire, or play fight games is forced to protect his forest friends from hunters.")
Dinosaurs from A to Z, Childrens Press (Chicago, IL), 1983.
Lenona.