Hello, I'm very concerned about your little one,Fluffy and I'd like to help.
Do you feel she is falling over because she is weak or because her sense of balance is off? If you look at her eyes are they moving back and forth or in a circular fashion in a rhythmic fashion? Does she have a head tilt or seem to be consistently falling to one side?
If she has a head tilt and her eyes are moving back and forth rhythmically, especially if you try and move her these symptom are a disturbance in her vestibular system, or the system that controls balance. It can signify a middle ear infection or a problem in her brain which "reads" signals from her middle ear. As you can imagine if you're dizzy you wouldn't feel like eating but it's very important that she continue to eat. If she doesn't her gut will shut down. If necessary force feed her ground pellets or vegetable baby food several times a day. And drinking when her balance is off will be difficult as well so you may need to help her with that as well.
There are two common reasons for a bunny to lose their balance. One is a middle ear infection with a bacteria called pasteurella, the other is a parasite in the brain called E. cuniculi. Other possibilities, especially in a young, developing bunny are head trauma or inadequate levels of vitamins A & E in their diet.
Bunnies often have the pasteurella bacteria in hiding and in times of stress (as little as change in weather or coming to a new home) it comes out and causes problems. Because bunnies produce inspisated pus (thick, cheesy) she'll need oral antibiotics to hit the middle ear.
E. cuniculi is passed bunny to bunny in the urine or very rarely from a mom to kits in utero. If this is her problem she probably had it when you got her. They can shed this parasite in cysts in the urine early in the infection process so if you have kids don't have the kids clean the cage.
She needs an examination by her veterinarian or a veterinarian that is comfortable treating rabbits. Most veterinarians will treat for both if there's any doubt which is present. I usually use Baytril in suspension for the bacteria and a "bendazole" to treat the parasite. It should be fairly straight forward and treatable if caught early. BUT some bunnies get secondary gut bacterial overgrowth when using oral antibiotics and some are left with a slight head tilt. So sometimes it's not as smooth as we hope.
Your veterinarian can also evaluate her for signs of trauma and discuss diet with you, recommending supplements if they believe she has a deficient diet.
Make sure her cage is kept very clean. Don't use wood chips as bedding though they carry bacteria and fungal spores.
If your veterinarian can see an external ear infection he or she will probably prescribe an ear drop too.
The other possibility for her condition is a severe intestinal parasite infestation or gut stasis due to bacterial overgrowth. These will make her very weak and thus unable to stay upright as well.
Ideally she would be seen by a veterinarian who is familiar with bunnies tonight. She is very young and just doesn't have reserves to draw on. If you don't have a rabbit veterinarian yet here is a link to help you find a rabbit veterinarian in your area: http://www.rabbit.org/vets/vets.html
Best of luck with your little one. Keep her warm and quiet until you can have her seen.