You could actually answer this question two ways.
First, George tells Lennie early in the story that one day he will get him a puppy:
Tell you what I’ll do, Lennie. First chance I get I’ll give you a pup. Maybe you wouldn’t kill it. That’d be better than mice. And you could pet it harder.
Lennie loves to pet small, soft things. The problem is that he doesn't realize his own strength, and his small pets, typically mice and rabbits, die quickly. George believes that if Lennie had a puppy, he would have the opportunity to enjoy petting it; since puppies are generally stronger than mice and rabbits, George is hopeful that Lennie wouldn't kill a larger pet.
George also hopes to get a farm for the two of them to live on someday, so this is a second way you could answer the question. Lennie is particularly excited about being able to feed and care for the rabbits and frequently asks George to tell him about their "someday" plans. George typically does so, giving Lennie a sense of hope that their current difficulties will lead to a brighter outcome. This plan gives both George and Lennie something to work toward, and this shared goal encourages them through some dark days. In fact, the final conversation between the men is about their dreams of a farm, a place where Lennie can tend rabbits and there "ain't gonna be no more trouble" for him.