I personally do not recommend keeping rabbits outside.
They are very very fragile animals, and while it can be done, you should really look at why you are keeping rabbits, and wether or not the risks are worth it.
If someone is keeping rabbits for meat, obviously they will not be living inside. If your a breeder you likely wont be keeping your rabbits indoors either. But, if you want one as a pet, I highly recommend you research the risks of keeping rabbits outdoors.
Rabbits are very very fragile. Temperature swings are a huge concern as they can go into heat stroke, or hypothermia very quickly. They become stressed out quite easily as well, and temperature is not good for that.
Not only are temperature swings a problem, but everything about a bunny is fragile. They can break their backs, and other bones in their body. This can be a death sentence for your rabbit. My bun Aspen suffered from spinal issues after I got her. I rescued her after she had been dumped, and her hips were the first indicator of an issue. After 6 months of owning her, she was euthanized because her back had gotten so bad.
Rabbits can also go into shock of a predator is near. They are prey animals, and there for predators are terrifying. Rabbits are not easy to recover from shock, and it can be a killer. If shock doesn't kill them, the fear from a predator trying to rip through a hutch could kill them before the predator. Heart attacks from fear are not uncommon in rabbits,
@EverythingDucks actually has a friend who this has happened too.
There are also lots of diseases rabbits can get, a big one being E.cuniculi. Its an infectious organism that gets to rabbits from infected grass. It causes neurological issues ranging from a mild head tilt, to seizures. It also can cause paralysis, hind leg weakness, cataracts, incontinence, and in very sever cases, rolling uncontrollably/seizures, and cataracts that mature so badly they rupture the eye lenses. Its a very extreme and illusive disease, not something you want to deal with.
Lastly, rabbits are also very social animals. They need attention if you are only getting one, and that attention must come from their people. Being outdoors is not going to give the rabbits the connection with their owners they need, and you may only be viewed as the food person. Rabbits can become very attached to their owners, when they do, they can be as friendly and social as a dog, maybe even more. If you want a connection like that with your bun, you will need to share a space. I saw above that you have allergies, so that probably isn't possible. With that in mind, consider again why you want a rabbit.
If its a pet, then if you want that special bond, it will need to live indoors, or you will need to live outdoors with it almost all the time. If that isn't possible, than your rabbit is not going to be the social pet your hoping for, rather a flighty yard ornament that might not be all the things you wished it would be before getting it.
Just something to think about.
With all the above in mind, people do keep rabbits outdoors without issues. Of course, these rabbits may not always be pets, and are likely being used for entirely different purposes, so keep that in mind.
To answer your question, yes, it is possible, but is it good for the rabbit? No. Is it good for the relationship I'm assuming you wish to have with your rabbit? No. Is it necessary? No. There are no pro's for the rabbit to keep it outdoors, maybe pros for your. Less mess, no cleaning, no potty issues, no destruction issues, etc, etc. But there are no pro's for the rabbit, and that is who we should be thinking about in this situation. With that said, I will always suggest you don't do it.