Vaccines should usually be given at the recommended ages and intervals, not earlier or later. The recommendations are derived from studies of measured antibody levels after vaccines were given at different ages, with the goal of providing the highest possible level of protection. So, for example, the HiB vaccine should not be given before six weeks of age and the rotavirus vaccine should not be given after thirty-two weeks of age.
In addition, many vaccines have recommended intervals between the original shots and the booster vaccines. The hepatitis A vaccine booster should be given more than six months after the original vaccine injection. There are rare exceptions to the rules (such as giving the measles vaccine to a child traveling to certain parts of the world), but those are clearly laid out in guidelines available to your doctor.
In addition, certain live-virus vaccines, such as MMR, varicella, shingles, nasal influenza, and yellow fever, have particular rules about how to space the vaccinations. Studies show that if two vaccines in this group are given on the same day or are given more than twenty-eight days apart, the resulting antibody levels are equivalent. However, if the two vaccines are given less than four weeks apart, the antibody response to the second vaccine is diminished, leading to suboptimal protection.