I have a Cape buffalo mount that I want to put on a pedestal.
Questions-
I’m thinking 30-36” diameter pedestal about 30” tall.
Do you need to put some weight in the pedestal to keep it from tipping over?

I have two of them and neither has weight added.

They are plenty stable.

Fine without weight while sitting still. Mine's wheeled. Without weight, I'd recommend removing the buffalo before moving the pedestal very far. Trust me on this, I'm never going to admit to details.

My base is wheeled, and I've never had any issues. But it has a granite top, so that might increase stability as the base does weigh quite a bit.