I suppose your decision also depends on how much time and attention you can devote to keeping her clean, dry ect in the condition that she is in. I know I wouldn't have the time, which sounds horrible, but is true. Also, just be careful as it may be more distressing for your child to watch the rabbit deterioate - I had many pets as a child, and the worst memories I have are of pets that took a long time to die, through age or illness - really horrible, and it stays with you. I had my beloved jack russel put to sleep, nearly 4 years ago, as his standard of life had got so bad, and he could hardly walk, see or eat. I'd had him since I was 15, and don't think I can ever get another dog even now, he was just my best mate. But I know I did the right thing. I felt more guilty watching how he struggled.
Good luck, it is very hard x