Awesome responses so far! Thanks for all the good ideas. I actually took this far enough to research facts about bunnies. Turns out they have nearly 360 degree vision, horrible/no depth perception, great hearing and smelling, and literally jump for joy. I'm glad to see someone has already thought of the bunny totem, as well.
I had thought about some kind of dodge ability, but I think giving a barbarian a bonus action dodge might be a bit overpowered on top of potential resistance to certain damage. I think x/day dodge may be more reasonable.
I like considering the psychology of fight-flight as well because my character doesn't necessarily want to go picking fights. It's just that her "flight" response is typically to kill every threat as quickly as possible. She is no saint...
I have looked at the other totems from SCAG, and I like all of them. I just think it's fun toss around ideas and see what we can come up with.
As of right now, I'm going to narrow it down to key words...
Speed
Jumping
Burrowing
Luck
Improved hearing and smelling
360 vision
I'm going to work with these and see if I can't come up with some balanced and fun attributes.
Oh, and from now on, the Monty Python bunny scene will forever remain in my head whenever I rage with this character!