Douglas County’s unemployment rate dipped to 12 percent in September, though job growth was flat, the Oregon Employment Department announced Tuesday. Slight job losses in the public sector were balanced by modest gains in the private sector to keep the county’s non-farm work force at 34,630, unchanged from August. The jobless rate in August was 12.4 percent. The unemployment rate a year ago was 13.2 percent. “Considering where Douglas County is coming from, this is a fairly good report,” state regional economist Brian Rooney said. “We’re starting to see manufacturing and construction come back and those industries were really hurt …