I totally second the polar bear request.
For the bunnies, I personally don't agree though. Desert bunnies are very easy to find in deserts, and respawn there as well AFAIK. The other types of bunnies might be slightly less common (although white bunnies in snow biomes are pretty common too), but can be acquired by breeding your other rabbits, in which there is a small chance of getting a new color.
Another suggestion from my side would be the Elder Guardian. Since the world has a border, there are only so many Ocean Monuments out there (of which I'd say the majority has been discovered) and there's head hunters out there killing them for the heads, like Angelina described for polarbears, combined with not respawning and the fact you can get an hidden advancement (How Did We Get Here) with one, I'd say this would be a valid option for spawn eggs too - albeit being very expensive, probably, to not flush the world with them (say, 50k?).
Two more suggestions I'd have are the Evoker and Vindicator. Again, the world has a border, and I reckon there aren't more than 2 or 3 Woodland Mansions out there. I'm not positive if there are mobheads out for these two mobs (or three, actually, counting the Vex that is spawned by Evokers), but if there are, they probably are a wanted item by headhunters too (and if they don't exist, I'd love them
). These mobs also do not respawn and aren't breedable, while they are useful for more creative ways (hostile and passive) mobfarm killing platforms, as well as collection/displaying purposes. Again, to not flush the world with them, they'd probably have some hefty prices (30k?).