If the barrel is Damascus twist steel, it's a lot older then 1945.
Damascus barrel production stopped sometime in the early 1900's.
Second, no one was making sporting guns in 1945, due to the War.
The problem with IDing and pricing the Ithaca doubles is, there were SO MANY models, versions, and grades made from 1888 to end of production in 1948.
Prices can run from around $300 up to $50,000.
Best advice I can offer is to buy a copy of "The Blue Book of Gun Values" at a book store and try to ID the exact model, version, and grade.