INSERT INTO queue (TransKey, CreateDateTime, Transmitted)
SELECT Id, '2013-12-19T19:47:33', 0
FROM trans WHERE Id != (SELECT TransKey from queue)
There are two different "flavors" of INSERT. The one you're using (VALUES) inserts one or more rows that you "create" in the INSERT statement itself. The other flavor (SELECT) inserts a variable number of rows that are retrieved from one or more other tables in the database.
While it's not immediately obvious, the SELECT version allows you to include expressions and simple constants -- as long as the number of columns lines up with the number of columns you're inserting, the statement will work (in other databases, the types of the values must match the column types as well).