Dremels are used on dog nails, parrot beak and parrot nails quite often on pets that will allow it or can be safely restrained without too much stress on the pet.
A dremel at a moderately high speed will actually create a some heat from the friction of grinding the nail- and can “cauterize” the quick- but only it it is just the tip- and even that is not a sure thing that it will not bleed. Dremeled nails don’t have the sharp edges like trimmed nails do. Some parrots that need routine beak/ and or nail grooming will actually start making the dremel noise before the dremel is even turned on.
I am not sure how well it would really work on a rabbit though- it takes longer to dremel off a length of nail than it does to cut it with clippers. If I dremel my dogs nails- I usually cut them first- otherwise it takes longer to dremel them. I have a battery operated one that is not as powerful as the plug-in version and I started them with that first- as it is smaller and not as scary.
So unless you were taking just a little bit off the bunnys nails or were just filing the edges smooth after a trim- I would not use it. And even then it might freak the bunny out too much. I have never tried the dremel on Cotton’s nails. I am so pleased when she does well for her trims with the nail trimmer- that I don’t really expect more than that.