Bunnies are NOT as resilient as people like to think.
They do better in the cold than heat. They can do fine without heat at 50F. There should be NO drafts in the room. Supplemental heat can be some blankets of it won't chew them or small animal heat pads. They don't do well 80F and up. Either provide a fan in the summer or keep it in a cooler room.
That hutch is way too small for bunnies unless it is use for a few hours a day. They usually spend the night foraging so while your daughter sleeps, it will need space to move. A minimum of space should be something that allows the bunny to hop 3 times its length, stand on its hind legs, and no bars for flooring as that can cause hock sores which are painful to your bunny. I use Wabbitat plus the extension which provide about 5-6 foot long of space, plus a puppy play pen, for my 3 lb bunny. This space is necessary as they need to exercise and move in order for their guts to function properly.
Bunnies are closely related to deer. They are grass eaters and their sensitive gut rely heavily on the diet provided. So hay is a must and it is to be provided 24/7. Do not feed alfalfa for adults. Do not use those yogurt drops treats from pet stores. Bunnies can survive strictly on hay. Pellets can be supplemented in very small amounts, no more than a few teaspoons a day. I recommend Oxbow for pellets due to its high fiber content. Veggies should be no more than the size of its head per day, and fruits given very sparingly or in small amounts or not at all.
Bunnies can do a lot of damage in less than 5 minutes, including but not limited to, chewing threw wires of all kinds, walls and carpets. I left my vacuum cleaner in my bunny's play pen for 3 min. I turn around to find its wire chewed half way through. Bunny proof your home prior to bringing it home.
Litterbox train from day one. It is optional but recommended for easy cleaning. Place it where it starts to pee then move it slowly by inches to your desired location. Use paper bedding or paper pellets. Pine pellets are okay but can be messy. Place hay on one side of the box.
Do not pick up your bunny unless 1. You know how to restrain it from hurting itself 2. You have to move the bunny 3. You earn its trust. Bunnies in general do not like being picked up. If picked up wrong, they can kick so hard to break its spine.
Find an exotic bunny vet near you now for when you need one. Like I mentioned, it is important to maintain good gut flora. If not, your bunny can become very sick with what we call 'poopy butt', which is fatal and can kill your bunny within 24 hours if no emergency care is given.
There is a reason why bunnies are #3 most surrendered pet in the US. People underestimate their