I can't predict what will happen, but I can tell you what happened with us.
Our son was afraid of dogs. Not severely, but the neighbor's little foo foo dog (a small wire haired terrior... less than 15 inches tall) jumped up on him and startled him, causing him to fall backwards and land on the concrete. It hurt. He was 5. He never cringed or clung to us around dogs after that, but was adamant that he didn't like dogs and that "Millie" was mean.
Our daughter, going on 3, LOVED Millie and every other animal she encountered. We decided we were going to get a dog. We did our research, and decided to find a German Shepherd pup. Got one just before daughter turned 3 and son turned 6. He was never afraid of her (she was only 10 weeks old and was very small when we got her...she was probably more scared of him when we brought her home--after the car ride alone in the crate). He was never afraid of her. She went through some puppyhood herding and nipping at their elbows (she is a herder after all)...but we worked through that and she matured and outgrew a lot of those behaviors as she learned that humans are "above" her in the pack.
He isn't afraid of dogs now. And never has been since. The kids do know to not approach a strange (unknown) dog. And to ask an owner first if they want to pet a dog. But they are not afraid. They curl up with her (she's 7 now, and big) in her bed sometimes, give her hugs, crawl under their bed with her, etc.
But that was our kid and our dog. Your story may go differently. But "fear" is one of the reasons we felt it was important to get a dog initially. Not, by any means the ONLY reason... but a contributory reason to go ahead with it. Our youngest was 3, but she is an animal lover and always has been, and is very mature for her age.