This answer is interpretive and contains a speculative analysis about Lennie and his motivations.
Lennie does not kill little animals accidentally. He tells George that he usually kills them because they struggle to get away and sometimes bite him. Lennie is looking forward to tending rabbits for two reasons. One is that he will have the pleasure of petting soft little animals. The other reason is that, since he is the one who tends the rabbits, he will be the one who kills them when they are fat enough to eat. In other words, he gets pleasure from petting little animals, and he also gets pleasure from killing them. This pleasure he derives from petting and killing animals is symptomatic of a violence which Lennie does not understand and which George does not suspect until he sees the dead body of Curley's young wife in the barn. George
...was down on his knees beside her. He put his hand over her heart. And finally, when he stood up, slowly and stiffly, his face was as hard and tight as wood, and his eyes were hard.
George is beginning to feel guilty of the girl's death because he brought Lennie to this ranch, because he protected him from the mob in Weed, and because he "should have knew" that Lennie was becoming dangerous. Lennie can't be blamed for being what he is, but that doesn't change what he has become.
"I should of knew," George said hopelessly. "I guess maybe way back in my head I did."
That is the most significant passage in the book. George "should have knew" that Lennie's violence couldn't be controlled. Perhaps Lennie was not interested in feeling the girl's soft dress, but he was sexually attracted to the girl herself. When she got the idea that he was trying to rape her, it might be she wasn't far from the truth--although Lennie himself probably didn't understand his own urges. George assumes that something similar happened with Curley's wife in the barn. Lennie didn't know what he was doing. Lennie is becoming a monster because he can't control his desires and his enormous physical strength.
The rabbits are so important to Lennie in Of Mice and Men because they represent, to him, home, safety, peace and love. Lennie is an innocent with the mental capacity of a child; he knows and believes only as much as George has told him. The one part of their dream that Lennie has latched onto is that of "tending the rabbit." If you will notice throughout the book, anytime there is a problem or trouble, this is Lennie's safe place. It is as if he withdraws and somehow uses this idea to calm and sooth himself. The rabbits are soft, smooth and comforting to him. On the other hand, though, they also represent a sense of fear with him because if he does something wrong, he is afraid that George won't let him "tend the rabbits." Even George uses this to "keep Lennie in line." Right up to the very end, taking care of the rabbits on their farm is the most important thing on Lennie's mind. You have to believe that before he dies in the end, as he looks across the river, he is imagining himself, once again, "tending the rabbits."
The rabbits are an essential part of the dream for Lennie. He frequently asks George to repeat the details about the farm they will someday own where he will get to "tend the rabbits." They are also an example of the small, soft animals Lennie likes to pet; others are the mice and the puppy. Unfortunately, he doesn't know his own strength; all of the animals he pets die. Therefore, Lennie thinks that because the rabbits are bigger animals, they won't die when he pets them. He is perhaps attracted to their softness because he yearns for some warmth and softness in his life. Since Aunt Clara died, he has no one to love him as she did. George looks after him, but he often complains about how his life would be different if he weren't responsible for taking care of Lennie. The rabbits represent Lennie's dream of a happy future.
Lennie craves contact with soft creatures; this is symbolic of his own soft hearted nature. Unfortunately, he is too strong and too "simple" to be able to treat these animals gently enough, and he eventually kills the animals he takes as pets. As George points out in Section 1, Lennie killed all the mice his Aunt Clara gave to him, and she eventually stopped giving live mice to him. Since the rabbits are larger and more able to endure the effects of his petting them, Lennie wants to have them available to him as pets. George talks with Lennie frequently about their raising rabbits on the farm they hope to own one day. Rabbits become the focus of Lennie's dreams, and they represent a part of the the elusive American dream.