Rabbit hair- is there a filter that works

Hi

Does anyone have a filter that will remove rabbit hair which is in the air and on floor?

I vacuum everyday, and have a filter running constantly in the room and we keep our mini lop ear bunny in a large back room, but her fine hair flies in the air. Her shedding makes a mess.

We love her but after 3 years we are almost fed up. Any advice on bunny proofing wooden molding too please.

Does anyone have a fiberglass wall bunny home?

Thank you for any help