Welcome to the forum.
Here is what one can conclude from what you have provided:
(1) The "Federal Law Forbids" text was required by US law during the 1930s to 60s on all spirits bottles, so your dating assumption is correct. Yes, this bottle might have contained whiskey but could also have been any other alcoholic drink.
(2) The D in D-9 indicated a distillery as opposed to a bottler. This is a bit confusing...read on.
(3) Ball Bros. Co. did operate throughout the 30s to 60s but is thought of as a manufacturer of canning jars (think Ball Perfect Mason) It is possible that they produced containers for other uses but it seems highly unlikely that they were also in the liquor manufacturing business.
A photo might help others piece together the significance of the marks - would be worth posting one if you can.