The first real question with a kitchen island is not how to move it, it is whether it is meant to move at all. Some are freestanding furniture on locking casters, others are cabinetry bolted to the floor or plumbed for a sink, and treating the second type like the first can crack a countertop or tear out plumbing.
Pro tip: If the countertop is stone, budget for a granite or quartz specialist to detach and reset it rather than risking a crack.
Watch out: Never try to move a built-in island yourself; cutting into cabinetry, plumbing, or electrical to free it is a job for a licensed contractor.