Hahaha the issue with a shedding rabbit in the house : D
Powder sheds like mad 24/7 365 and his fur gets into my computer quite a bit. Depending on your case, there are some things you can do though.
For side/front intake fans you can buy the kind that has very small holes to filter dust and such in front of the fans. That will cut the majority of the fur out of your system, as it gets sucked up in the intake but stays on the outside since the holes are too small for it to get through. It doesn’t cut enough air to overheat, it helps keep down dust so it actually helps the heat issues. They use those types of fans for intake in a lot of gaming cases.
For the back fans that push air OUT you don’t want to obstruct them in any way. That will cause heating issues.
Otherwise, get a can of compressed air and keep it on your desk. When fur starts building up, just turn the PC off and shoot the air into it to clean it out. Every month or so give it a better clean. If fur and dust are REALLY bad and it’s a desktop, you may every few years need to do a full cleaning to avoid overheating, which requires taking the fan off the CPU and cleaning the dust/fur out of the heatsink. If you’re not comfortable doing that (you can break your CPU if you don’t know how to safely remove the heat sink) then you can get it done if it comes to it. But, usually you’re safe just air compressing it. My partner’s heatsink filled up with dust earlier this year though and had to take it apart cause his PC was overheating all the time.
If it’s a laptop, compressed air and a vacuum and try to keep it off your clothes/couches as it can suck in the fur from those surfaces (and we all know if you live with bunnies, you have fur on your clothes and furniture haha)