Timothy is actially a very common allergen – I have problems with it. But it can be managed with some thought and care
1) I made a hay rack – it is closed on 4 sides and the side is covered with a NIC grid panel. Pepper pulls the hay out from between the grids. I have it set up over the litterbox so that andy extra bits or dust fall down into the box. I made it big enough that I only have to fill it once a week or so, and then I fill it quickly and then go wash my arms and face to get the hay dust off.
2) I run my Roomba regularly, and being able to set it running and then leave the room keeps my symptoms low. If you have carpets, this might be harder – you’d need a good vacuum (mine has a washable HEPA filter). Also, I empty the dirt cups promptly down the toilet, so there isn’t any dust lying around in the trash cans. Because of my other allergies I also have all hardwood or tile floors with rugs than can be washed in hot water and furniture that is either leather, wood, or has removeable-and-washable covers.
3) A good air filter may help if you have symptoms when you’re not touching the hay.
I knew I’d be dealing with this when I first thought about getting a bunny, so I put plenty of thought into figuring out how I could work around my limitations. It’s not perfect – I will always have to take prescription medicine but that woule be the case with or without the bunny.