Heck, ya! Most rabbits will go through an annual moult. Sometimes it looks awful, sometimes you'll hardly notice. Depends on the rabbit and sometimes the weather. It's the end of August here and my rabbits are in full moult!
Here's poor Chester. He moults all over, all at once. This is a picture before his second brushing.
Here is after his brushing. He's not overly impressed with me, but he looks grumpy on a good day.
Here's poor Levi before his brushing. He starts moulting from his head back. This is his first moult, he's a year old.
Here's most of the fur from Chester's brushing. Mind you, this is a two pound rabbit. Bigger rabbits, more fur.
Some rabbits don't moult so drastically. This is Luna's litter pan. Other than some loose fur strands, and this fluff in the pan, you wouldn't even know she was moulting.
Rabbits should be brushed on occasion. But when they moult, you will need to brush them. Rabbits will try to clean themselves but when they moult, it's a lot more fur. When they ingest that much fur, it can cause a blockage. Unlike cats, rabbits can't vomit. So the blockage stays there and that can be deadly. You will not be able to brush it all out at once. You may need to do it several times over the course of a week or even several weeks. Making sure the rabbit has lots of fibre is also important. Hay is great for this.
If you suspect wool block, you should consult a rabbit-savvy vet. Less interest in food, smaller droppings, less droppings, lethargy. In the mean time, you can remove pellets and feed hay. Some claim papaya and pineapple help with moving a blockage along. I have not had this issue so I have not tried it myself, so I can't comment any further. Woolly and Angora breeds are more prone to wool block.
Rex rabbits also moult but brushing them can ruin that beautiful coat. Take a damp cloth or damp hands and just run your hands over them to remove any loose fur.
Just FYI, here's my favourite brush! https://www.amazon.ca/gp/aw/d/B00VBR10K0/ref=mp_s_a_1_3?ie=UTF8&qid=1503852514&sr=8-3&pi=AC_SX236_SY340_QL65&keywords=the+furminator&dpPl=1&dpID=41LXrbTcpfL&ref=plSrch
Ive already talked about basic rabbit care. Now I want to focus on housing. Keep in mind that I am a breeder, and although many people keep rabbits as pets, they ARE considered livestock.
Size: The larger the rabbit, the larger the space needs to be. The more space you can offer, the better. I raise Netherland Dwarfs. They are fine housed in a cage 18x24. I like 24x24, myself. Flemish Giants on the other hand should be in a space 48x48. Before picking a breed to bring home, make sure you research the size of the cage needed. Also, if you only have the bare minimum for a cage size for the breed you pick, it's nice to let them out for a little play time and exercise.
Type: There are many types of housing you can use for rabbits. The number one concern would be that it is safe. I use wire cages with wire bottoms for most of my rabbits. Again, different breeds require different set ups. My cages have trays under them, but you can also get them without trays that you can hang. This way the rabbit never comes in contact with their own feces and urine, which is way more sanitary. This makes for a cleaner rabbit and helps prevent urine scald on their feet. You just dump the trays out and occasionally give them a spray and a little scrub and you're good to go!
I've tried wire cages with solid bottoms, thinking hey would be better for babies, but a had a new water bottle leak when I wasn't home in the winter and I lost half my babies. So I sold those and changed to all wire bottoms. Wire bottoms also allow for better air circulation for cooling in the summer.
You can get these from many cages builders. http://www.sunnymeadowscages.com/single-level-homes.html
I have some rabbits in pens on the floor that are attached to outside runs. These are all made with hardware cloth and even the run has hardware cloth on the bottom. DO NOT use chicken wire! Rabbits can chew through it, weasels can go through it, raccoons and rip threw it. The only thing that chicken wire should be use for is to keep chickens out of the garden. My Flemish Giant is in one of these pens. Heavier breeds may find wire bottoms hats on their feet. There are also some breeds, like Mini Rex, that have thinner fur on their feet which makes wire hard on them, resulting in sore hocks. My Mini Rex is in a wire bottomed cage, so he has a resting mat he can sit on which makes it safer and easier for him.
Some people choose to raise their rabbits in hutches. For raising outside, these usually have one or many compartments with solid roof and sides with wire front and bottom to allow for air flow and for the droppings to fall through, and you just shovel them up and dispose of it or compost it. (Rabbit manure is great for the garden!) Inside hutches usually have solid bottoms, that you will need to fill with litter (like pine shavings). Some hutches are multilevel to allow the rabbit more space and exercise without taking up more floor space. For outdoor hutches, it is wise to cover the wired front with plastic to prevent the cold wind from blowing on them. Rabbits should always have a place to get out of the wind.
Many pet rabbit owners keep their rabbits in wire cages with plastic bottoms that you can buy at any pet store. Again, you will some sort of litter for these. Many rabbits will use litter boxes, though there will still be the occasional dropping in other places, but most rabbits pick a corner to urinate it, so you can just put a litter box in that corner and dump it out every other day.
Two examples of hutches (pictures from Wayfair)
Plastic bottomed cage (Wayfair)
Large homemade hutch (google images)
My rabbits are housed in a building. They are protected from the elements. If you choose to house them in outside hutches, make sure they are protected from the elements but still have good airflow. If you have them in your house, make sure they are not just shoved in a room where you only go in long enough to feed them. Because really, what's the point of having the rabbit?
Rabbits are incredibly cold tolerant, but are sensitive to heat. Do not leave your rabbit outside in the direct sun where they can not get into shade. Rabbits can suffer from heatstroke very easily. Rabbits do not need heat in the winter, just some place that is draft free. If you have a heater in your building and the power goes out, then the shock of the temperature drop could be very hard on them. In the summer, I use large fans and frozen ice bottles to help cool them down.
If you choose to house you rabbit outside and bring them inside for the winter, do so before the temperature drops too much. Taking them from cold to a place that's heated, you cause them to have a heatstroke.
More than one rabbit?
Rabbits should be housed separately. Many rabbits are very territorial and will not tolerate another rabbit in their space. There are always exceptions, but generally they should be housed separately. Hutches can be built with separate compartments for each rabbit. If you have smaller spaces, they should each have their own cage. They can be next to each other and eventually they may be allowed supervised playtime together and you can take it from there. Some rabbit Breeders have colonies set up up that house several does (females) and one Buck (male). These spaces need to be very large with smaller compartments that each doe can use as a nesting area. I do not have much experience with colonies so I can't comment further.
Silver Fox colony
As long as your rabbit has enough space, and a place to get out of the weather when they need to. Someplace dry and draft free. Someplace safe and secure and clean, you're rabbit should be happy. Now all they need is some food, water and some love.