Why not take an animal your family members aren't allergic to? Like a guinea pig or something. I'm really not a fan of the idea of keeping a rabbit outdoors. The cold kills, but it kills less than the heat. Last summer was quite hot and I've seen several posts about oudoor rabbits dying from heat stroke or fly strikes.
That's not even considering the fact that keeping rabbits outside attract rats, which can be a danger for the rabbits and is not the kind of things I want in my garden.
Rabbits have to be outside of their cage / hutch at the very least 5 hours a day (which is not much to begin with) to avoid making them go mad and physical problems like pododermatitis, obesity... Where will you let your rabbit run when it's raining?
Will you want to go outside to feed the rabbit / clean the cage when it's dark outside, cold and damp? What about in a year? In ten years? I certainly wouldn't. And that's how a lot of bunnies end up being neglected.
I'm not saying that there aren't people taking good care of outside rabbits or that some installations aren't good, but there is a lot of planning and dedication involved. You should really think hard about what you are doing before attempting it. Rabbits are expensive to maintain (if you get a girl, you'll have to spay her to avoid uterine and ovarian cancers... the risk being over 80% on an intact doe), mine cost me more than the cat or the medium sized dog. I feel like I have to precise here: rabbit's need their size in hay, about 8% of their weight in fresh vegetables and some good quality pellets everyday (so, flemish giants being big rabbits they eat quite a lot). They also can live for over 10 years so it's a long term commitment.
I would also advise against keeping a rabbit, especially an outside rabbit who will spend most of his days alone, as a single rabbit. He will get dead bored. He will need a friend to keep him company. So, spay and neuter if it's not a couple from a shelter (I'd say it will cost you around 400 $) and twice the expense.
I suggest you go read the House Rabbit Society Website before deciding if you really want to go the rabbit route. And don't hesitate to ask questions on the forum:
http://rabbit.org/before-you-adopt-2/