I just found this topic today, so I'm way behind the curve. If I had gotten in at the beginning, I would have mentioned what was so obvious to me, BIRDS! Hawks, Eagles and Owls all eat rabbits. I think owls would be fun.
Here's a quick and dirty logo sketch I made on MS paint. The owl needs a bit of work on the proportions, but I like the dead rabbit...
If I have time I'll render it in vector graphics:
Anyway, there was also mention of ship logos. I have one already for a GM custom I planned before the AOZ contest:
In Gundam 0083 there's the Albion, named after a mythical island. So I went with another mythical island, Avalon, where Excalibur came from, hence the sword.
I also have several basic AEUG logos and texts for AEUG weapons.