Murray the Cat/Federal logo
A transitional logo amending the pre-existing Murray the Cat design.
Many issues were actually cover-dated March-April or April-May 1983
Federal Comics FC (red and blue) logo
July 1983-January 1984
The first fully-fledged Federal Comics logo
Federal Comics FC (black and white) logo
A distinct short-lived variation on the FC logo
Australian Edition DC logo
March 1984-June 1985
DC replaces FC in the circle, and Australian Edition replaces Federal Comics in the outer ring
July 1985-March 1986
Australian Edition tagged alongside the standard DC logo
Clearly the logo story outlined here begins earlier, not just with the Murray variations but with Planet Comics and the Colour Comics Pty. Ltd. branding, but for the moment we are just concerned with the Federal Comics period.
With most of these changes there is a transitional month in which both logos appear. I've noted above the ones which cross over in my data - January 1984 and March 1984 - but I wouldn't be surprised to find crossover instances in June-July 1983 and June-July 1985.
The DC bullet logo appears in random colours - blue, red and black being the most common, but I've seen a pink one, and there may be other others. I doubt there's an underlying pattern to them.
The above images are placeholder samples pending clear high-resolutions samples of each without the masthead intruding.
Obviously the Federal Marvel editions have a different logo story.