Hi!
I'm from Michigan Rabbit Rescue and the House Rabbit Society, and hopefully I'll be able to answer your questions.
First and foremost, rabbits are the absolute worst pet for children, especially those under 10 years of age. They do not like being held, chased after, layed on, squeezed, or anything else of that nature which children are tempted to do to an animal. Children are also loud and spontaneous, which scares the living daylights out of 99% of rabbits. Definitely house the rabbit somewhere your daughter can't readily get at. I suggest you read this article about rabbits and kids: So Your Child Wants A Rabbit?.
Regardless of how much you paid for the rabbit, you got it from a pet store, which is, in all truth, the worst place to buy any kind of animal, including rodents such as rats, gerbils, and hamsters. It's never the optimum care that they need, but instead, usually cramped, dirty cages, with too many cage mates. This type of environment can cause many different sicknesses and symptoms. Be glad you got a healthy rabbit. I would highly suggest, though, that you take him/her to a rabbit-savvy vet for a check up. Although it would seem like all vets know about rabbits, most of the time they don't, even if they say they're familiar with them. Rabbit's physiology, care, and dietary needs are very different than that of a dog or cat's. Rabbits need exotic animal specialists. To find a good rabbit vet in your area, check this vet recommendation list at the House Rabbit Society: Veterinary Recommendations. One month is early enough to sex a rabbit, which the vet will do for you. Around 6 months of age, it is a very good idea to get your rabbit altered (neutered/spayed), since this reduces a lot of behavioral and health problems. If you ever decide to get another rabbit, I would highly recommend you check local shelters, Humane Societies, and private rescues. There's thousands upon thousands of rabbits euthanized every year because no one is adopting them, and buying from a pet store or from a breeder is just adding to the problem. More over, adopting a rabbit from a shelter or rescue will cost the same amount you paid at the pet store, but the rabbit will most likely already be neutered/spayed, and will have a clean bill of health.
Hopefully you read up beforehand on the rabbit diet, but if not, I will quickly go over that for you. A rabbit's diet should consist of three things, in this order: Grass hay, fresh greens/vegetables, and pellets. Since your rabbit is so young, it should receive unlimited pellets. Once he/she reaches 7-8 months old, though, you cut the pellets back to about 1/4 cup. Along with that, your rabbit should be getting both alfalfa hay and timothy hay -- alfalfa is a legume hay, not grass hay, which has more calcium and protein for growing rabbits. Around 8 months of age, gradually reduce the amount of alfalfa given until you have completely removed it from the rabbit's diet, and up the intake of timothy hay. At all times, a rabbit must have unlimited amounts of timothy hay. At around 6 months of age, you should start introducing fresh greens to the rabbit's diet. Some rabbit-okay veggies include romaine lettuce, green leaf, red leaf, escarole, endive, boston lettuce, dandelion greens, parlsey, cilantro, and basil. All changes in an animal's diet must be made slowly, so start feeding veggies as a treat before giving him/her the usual amount of 3-6 cups chopped veggies (3-4 different kinds, preferrably) daily. For more diet information, read this page: FAQ: Diet. Pet store feeds are very unhealthy for rabbits, especially the "gourmet" mixes with nuts, seeds, dried fruit/vegetables, beans, et cetera. You want JUST pellets. You should check out the two best brands of hay and pellets, Oxbow and American Pet Diner. To someone who is new to owning an exotic animal (rabbits aren't really exotic, but to most people's ideals, anything besides a cat or dog is "exotic" ), their food is going to naturally cost more. Buying hay in bulk will cut down food costs a lot. Two 10 lb boxes of hay from American Pet Diner usually costs me around $50, and will last 3 months. Since your rabbit is much younger, it will most likely last a lot longer. Getting a 10 lb box of timothy and a 10 lb box of alfalfa hay would be a very good idea. Also, Oxbow carries the best pellets for rabbits. They're the most recommended brand by rabbit specialists and veterinarians. There are two types of pellets: alfalfa-based, and timothy-based. Like I mentioned above, alfalfa is very fattening and high in calcium. For a young rabbit, this is good for them. Once they reach 8 months of age, though, and are full grown, they no longer need the extra calories or calcium, and this is when you switch over to timothy pellets, which have more fiber and are much less fattening. Buying pellets in bulk isn't such a good idea, though, since the general rule with them is to buy only what you'll use in 6 weeks time.
Aspen bedding is VERY light. Rabbits naturally like to dig, and many rabbits find that their litter boxes fit the bill for a perfect digging area. I would suggest you get an actual cat litter box, since they are larger and have higher sides, and use a heavier litter, such as Yesterday's News. Putting lots of hay on one side of the rabbit's litter box makes it a great treat for jumping in and using it for the rabbit. Rabbits have a natural tendency to eat and eliminate at the same time, so this helps that desire.
You can get your rabbit a regular cat bed if you feel he/she wants something to snuggle with, but most of the time, rabbits will either pee on them or chew them. I would suggest testing your rabbit's personality out by putting a couple folded towels on the bottom of the cage, and seeing if he/she will lay on them, or pee/chew on them.
Although it seems like she has a good sized cage currently, rabbits are VERY active animals, and need a LOT of time out of their cage. I would suggest you buy a large puppy pen (not a "small animal" pen, since even hamsters can easily jump out of them) for the rabbit to play in for 4-6 hours a day, or even live in once he/she is litter box trained. You should seriously consider bunny-proofing the room you have your rabbit in, and letting him/her freely roam around (that is, once the rabbit's fully litter box trained). It's not uncommon for people to bunny-proof their whole house and let their rabbits run around as a cat or dog would, either.
Hopefully I've answered your questions!