Ethical ownership of a rabbit?

Hi hi, I (26) have a circadian rhythm disorder which means that I can't produce enough melatonin to hold a sleep schedule. This means that every day I'm up 2 to 3 hours later and I sleep 2 to 3 hours later. Whenever I had a sleep chart going my sleeping times looked like a barbershop pole lol. Usually I go through the cycle twice a month, meaning half of the month I'm up during the day and the other half I'm up overnights.

I don't own any pets because of this, because I'm worried I can't ethically have one while not matching a schedule for it. Do you think this would affect a rabbit? I've been reading that some take naps every hour, some sleep 6 hours in a row and some adhere to your sleeping schedule. That's the one I'm worried about as I wouldn't want to stress the poor thing out.

I would take other pet recommendations as well!